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Chaos and Fractals [[electronic resource] ] : An Elementary Introduction
| Chaos and Fractals [[electronic resource] ] : An Elementary Introduction |
| Autore | Feldman David P |
| Pubbl/distr/stampa | Oxford, : OUP Oxford, 2012 |
| Descrizione fisica | 1 online resource (431 p.) |
| Disciplina | 515.39 |
| Soggetto topico |
Chaotic behavior in systems
Differentiable dynamical systems Fractals |
| ISBN |
1-283-64388-X
0-19-163752-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; I: Introducing Discrete Dynamical Systems; 0 Opening Remarks; 0.1 Chaos; 0.2 Fractals; 0.3 The Character of Chaos and Fractals; 1 Functions; 1.1 Functions as Actions; 1.2 Functions as a Formula; 1.3 Functions are Deterministic; 1.4 Functions as Graphs; 1.5 Functions as Maps; Exercises; 2 Iterating Functions; 2.1 The Idea of Iteration; 2.2 Some Vocabulary and Notation; 2.3 Iterated Function Notation; 2.4 Algebraic Expressions for Iterated Functions; 2.5 Why Iteration?; Exercises; 3 Qualitative Dynamics: The Fate of the Orbit; 3.1 Dynamical Systems
3.2 Dynamics of the Squaring Function3.3 The Phase Line; 3.4 Fixed Points via Algebra; 3.5 Fixed Points Graphically; 3.6 Types of Fixed Points; Exercises; 4 Time Series Plots; 4.1 Examples of Time Series Plots; Exercises; 5 Graphical Iteration; 5.1 An Initial Example; 5.2 The Method of Graphical Iteration; 5.3 Further Examples; Exercises; 6 Iterating Linear Functions; 6.1 A Series of Examples; 6.2 Slopes of +1 or -1; Exercises; 7 Population Models; 7.1 Exponential Growth; 7.2 Modifying the Exponential Growth Model; 7.3 The Logistic Equation; 7.4 A Note on the Importance of Stability 7.5 Other r ValuesExercises; 8 Newton, Laplace, and Determinism; 8.1 Newton and Universal Mechanics; 8.2 The Enlightenment and Optimism; 8.3 Causality and Laplace's Demon; 8.4 Science Today; 8.5 A Look Ahead; II: Chaos; 9 Chaos and the Logistic Equation; 9.1 Periodic Behavior; 9.2 Aperiodic Behavior; 9.3 Chaos Defined; 9.4 Implications of Aperiodic Behavior; Exercises; 10 The Butterfly Effect; 10.1 Stable Periodic Behavior; 10.2 Sensitive Dependence on Initial Conditions; 10.3 SDIC Defined; 10.4 Lyapunov Exponents; 10.5 Stretching and Folding: Ingredients for Chaos 10.6 Chaotic Numerics: The Shadowing LemmaExercises; 11 The Bifurcation Diagram; 11.1 A Collection of Final-State Diagrams; 11.2 Periodic Windows; 11.3 Bifurcation Diagram Summary; Exercises; 12 Universality; 12.1 Bifurcation Diagrams for Other Functions; 12.2 Universality of Period Doubling; 12.3 Physical Consequences of Universality; 12.4 Renormalization and Universality; 12.5 How are Higher-Dimensional Phenomena Universal?; Exercises; 13 Statistical Stability of Chaos; 13.1 Histograms of Periodic Orbits; 13.2 Histograms of Chaotic Orbits; 13.3 Ergodicity; 13.4 Predictable Unpredictability 16.6 Fractals, Defined Again |
| Record Nr. | UNINA-9910826490003321 |
Feldman David P
|
||
| Oxford, : OUP Oxford, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos and fractals : an elementary introduction / David P. Feldman
| Chaos and fractals : an elementary introduction / David P. Feldman |
| Autore | Feldman, David P. |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford : Oxford University Press, c2012 |
| Descrizione fisica | xxi, 408 p. : ill. ; 25 cm |
| Disciplina | 514.742 |
| Soggetto topico |
Fractals
Chaotic behavior in systems |
| ISBN |
9780199566440 (pbk.)
9780199566433 (hbk.) |
| Classificazione |
AMS 28A80
AMS 37-01 LC QA614.86.F45 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002578729707536 |
|
Feldman, David P.
|
||
| Oxford : Oxford University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Chaos and fractals : new frontiers of science / Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe
| Chaos and fractals : new frontiers of science / Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe |
| Autore | Peitgen, Heinz-Otto |
| Pubbl/distr/stampa | New York : Springer-Verlag, c1992 |
| Descrizione fisica | xvi, 984 p., [24] p. of plates : ill. (some col.), maps ; 24 cm. |
| Disciplina | 514.742 |
| Altri autori (Persone) |
Jurgens, Hartmutauthor
Saupe, Dietmarauthor |
| Soggetto topico |
Chaotic behavior in systems
Fractals |
| ISBN | 0387979034 |
| Classificazione |
AMS 28A80
QA614.86.P43 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000739429707536 |
|
Peitgen, Heinz-Otto
|
||
| New York : Springer-Verlag, c1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Chaos and fractals [[electronic resource] ] : a computer graphical journey : ten year compilation of advanced research / / edited by Clifford A. Pickover
| Chaos and fractals [[electronic resource] ] : a computer graphical journey : ten year compilation of advanced research / / edited by Clifford A. Pickover |
| Pubbl/distr/stampa | Amsterdam ; ; New York, : Elsevier, 1998 |
| Descrizione fisica | 1 online resource (469 p.) |
| Disciplina | 006.6 |
| Altri autori (Persone) | PickoverClifford A |
| Soggetto topico |
Computer graphics
Fractals |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-02621-2
9786611026219 0-08-052886-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; CHAOS AND FRACTALS; Copyright Page; Preface; Introduction; Contents; Part I: Geometry and Nature; Chapter 1. Chaos game visualization of sequences; Chapter 2. Tumor growth simulation; Chapter 3. Computer simulation of the morphology and development of several species of seaweed using Lindenmayer systems; Chapter 4. Generating fractals from Voronoi diagrams; Chapter 5. Circles which kiss: a note on osculatory packing; Chapter 6. Graphical identification of spatio-temporal chaos; Chapter 7. Manifolds and control of chaotic systems
Chapter 8. A vacation on Mars - an artist's journey in a computer graphics worldPart II: Attractors; Chapter 9. Automatic generation of strange attractors; Chapter 10. Attractors with dueling symmetry; Chapter 11. A new feature in Henon's map; Chapter 12. Lyapunov exponents of the logistic map with periodic forcing; Chapter 13. Toward a better understanding of fractality in nature; Chapter 14. On the dynamics of real polynomials on the plane; Chapter 15. Phase portraits for parametrically excited pendula: an exercise in multidimensional data visualisation Chapter 16. Self-reference and paradox in two and three dimensionsChapter 17. Visualizing the effects of filtering chaotic signals; Chapter 18. Oscillating iteration paths in neural networks learning; Chapter 19. The crying of fractal batrachion 1,489; Chapter 20. Evaluating pseudo-random number generators; Part III: Cellular Automata, Gaskets, and Koch Curves; Chapter 21. Sensitivity in cellular automata: some examples; Chapter 22. One tub, eight blocks, twelve blinkers and other views of life; Chapter 23. Scouts in hyperspace; Chapter 24. Sierpinski fractals and GCDs Chapter 25. Complex patterns generated by next nearest neighbors cellular automataChapter 26. On the congruence of binary patterns generated by modular arithmetic on a parent array; Chapter 27. A simple gasket derived from prime numbers; Chapter 28. Discrete approximation of the Koch curve; Chapter 29. Visualizing Cantor cheese construction; Chapter 30. Notes on Pascal's pyramid for personal computer users; Chapter 31. Patterns generated by logical operators; Part IV: Mandelbrot, Julia and Other Complex Maps Chapter 32. A tutorial on efficient computer graphic representations of the Mandelbrot setChapter 33. Julia sets in the quaternions; Chapter 34. Self-similar sequences and chaos from Gauss sums; Chapter 35. Color maps generated by ""trigonometric iteration loops""; Chapter 36. A note on Halley's method; Chapter 37. A note on some internal structures of the Mandelbrot set; Chapter 38. The method of secants; Chapter 39. A generalized Mandelbrot set and the role of critical points; Chapter 40. A new scaling along the spike of the Mandelbrot set; Chapter 41. Further insights into Halley's method Chapter 42. Visualizing the dynamics of the Rayleigh quotient iteration |
| Record Nr. | UNINA-9910457279103321 |
| Amsterdam ; ; New York, : Elsevier, 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos and fractals [[electronic resource] ] : a computer graphical journey : ten year compilation of advanced research / / edited by Clifford A. Pickover
| Chaos and fractals [[electronic resource] ] : a computer graphical journey : ten year compilation of advanced research / / edited by Clifford A. Pickover |
| Pubbl/distr/stampa | Amsterdam ; ; New York, : Elsevier, 1998 |
| Descrizione fisica | 1 online resource (469 p.) |
| Disciplina | 006.6 |
| Altri autori (Persone) | PickoverClifford A |
| Soggetto topico |
Computer graphics
Fractals |
| ISBN |
1-281-02621-2
9786611026219 0-08-052886-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; CHAOS AND FRACTALS; Copyright Page; Preface; Introduction; Contents; Part I: Geometry and Nature; Chapter 1. Chaos game visualization of sequences; Chapter 2. Tumor growth simulation; Chapter 3. Computer simulation of the morphology and development of several species of seaweed using Lindenmayer systems; Chapter 4. Generating fractals from Voronoi diagrams; Chapter 5. Circles which kiss: a note on osculatory packing; Chapter 6. Graphical identification of spatio-temporal chaos; Chapter 7. Manifolds and control of chaotic systems
Chapter 8. A vacation on Mars - an artist's journey in a computer graphics worldPart II: Attractors; Chapter 9. Automatic generation of strange attractors; Chapter 10. Attractors with dueling symmetry; Chapter 11. A new feature in Henon's map; Chapter 12. Lyapunov exponents of the logistic map with periodic forcing; Chapter 13. Toward a better understanding of fractality in nature; Chapter 14. On the dynamics of real polynomials on the plane; Chapter 15. Phase portraits for parametrically excited pendula: an exercise in multidimensional data visualisation Chapter 16. Self-reference and paradox in two and three dimensionsChapter 17. Visualizing the effects of filtering chaotic signals; Chapter 18. Oscillating iteration paths in neural networks learning; Chapter 19. The crying of fractal batrachion 1,489; Chapter 20. Evaluating pseudo-random number generators; Part III: Cellular Automata, Gaskets, and Koch Curves; Chapter 21. Sensitivity in cellular automata: some examples; Chapter 22. One tub, eight blocks, twelve blinkers and other views of life; Chapter 23. Scouts in hyperspace; Chapter 24. Sierpinski fractals and GCDs Chapter 25. Complex patterns generated by next nearest neighbors cellular automataChapter 26. On the congruence of binary patterns generated by modular arithmetic on a parent array; Chapter 27. A simple gasket derived from prime numbers; Chapter 28. Discrete approximation of the Koch curve; Chapter 29. Visualizing Cantor cheese construction; Chapter 30. Notes on Pascal's pyramid for personal computer users; Chapter 31. Patterns generated by logical operators; Part IV: Mandelbrot, Julia and Other Complex Maps Chapter 32. A tutorial on efficient computer graphic representations of the Mandelbrot setChapter 33. Julia sets in the quaternions; Chapter 34. Self-similar sequences and chaos from Gauss sums; Chapter 35. Color maps generated by ""trigonometric iteration loops""; Chapter 36. A note on Halley's method; Chapter 37. A note on some internal structures of the Mandelbrot set; Chapter 38. The method of secants; Chapter 39. A generalized Mandelbrot set and the role of critical points; Chapter 40. A new scaling along the spike of the Mandelbrot set; Chapter 41. Further insights into Halley's method Chapter 42. Visualizing the dynamics of the Rayleigh quotient iteration |
| Record Nr. | UNINA-9910784433703321 |
| Amsterdam ; ; New York, : Elsevier, 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos and fractals [[electronic resource] ] : a computer graphical journey : ten year compilation of advanced research / / edited by Clifford A. Pickover
| Chaos and fractals [[electronic resource] ] : a computer graphical journey : ten year compilation of advanced research / / edited by Clifford A. Pickover |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; New York, : Elsevier, 1998 |
| Descrizione fisica | 1 online resource (469 p.) |
| Disciplina | 006.6 |
| Altri autori (Persone) | PickoverClifford A |
| Soggetto topico |
Computer graphics
Fractals |
| ISBN |
1-281-02621-2
9786611026219 0-08-052886-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; CHAOS AND FRACTALS; Copyright Page; Preface; Introduction; Contents; Part I: Geometry and Nature; Chapter 1. Chaos game visualization of sequences; Chapter 2. Tumor growth simulation; Chapter 3. Computer simulation of the morphology and development of several species of seaweed using Lindenmayer systems; Chapter 4. Generating fractals from Voronoi diagrams; Chapter 5. Circles which kiss: a note on osculatory packing; Chapter 6. Graphical identification of spatio-temporal chaos; Chapter 7. Manifolds and control of chaotic systems
Chapter 8. A vacation on Mars - an artist's journey in a computer graphics worldPart II: Attractors; Chapter 9. Automatic generation of strange attractors; Chapter 10. Attractors with dueling symmetry; Chapter 11. A new feature in Henon's map; Chapter 12. Lyapunov exponents of the logistic map with periodic forcing; Chapter 13. Toward a better understanding of fractality in nature; Chapter 14. On the dynamics of real polynomials on the plane; Chapter 15. Phase portraits for parametrically excited pendula: an exercise in multidimensional data visualisation Chapter 16. Self-reference and paradox in two and three dimensionsChapter 17. Visualizing the effects of filtering chaotic signals; Chapter 18. Oscillating iteration paths in neural networks learning; Chapter 19. The crying of fractal batrachion 1,489; Chapter 20. Evaluating pseudo-random number generators; Part III: Cellular Automata, Gaskets, and Koch Curves; Chapter 21. Sensitivity in cellular automata: some examples; Chapter 22. One tub, eight blocks, twelve blinkers and other views of life; Chapter 23. Scouts in hyperspace; Chapter 24. Sierpinski fractals and GCDs Chapter 25. Complex patterns generated by next nearest neighbors cellular automataChapter 26. On the congruence of binary patterns generated by modular arithmetic on a parent array; Chapter 27. A simple gasket derived from prime numbers; Chapter 28. Discrete approximation of the Koch curve; Chapter 29. Visualizing Cantor cheese construction; Chapter 30. Notes on Pascal's pyramid for personal computer users; Chapter 31. Patterns generated by logical operators; Part IV: Mandelbrot, Julia and Other Complex Maps Chapter 32. A tutorial on efficient computer graphic representations of the Mandelbrot setChapter 33. Julia sets in the quaternions; Chapter 34. Self-similar sequences and chaos from Gauss sums; Chapter 35. Color maps generated by ""trigonometric iteration loops""; Chapter 36. A note on Halley's method; Chapter 37. A note on some internal structures of the Mandelbrot set; Chapter 38. The method of secants; Chapter 39. A generalized Mandelbrot set and the role of critical points; Chapter 40. A new scaling along the spike of the Mandelbrot set; Chapter 41. Further insights into Halley's method Chapter 42. Visualizing the dynamics of the Rayleigh quotient iteration |
| Record Nr. | UNINA-9910822919603321 |
| Amsterdam ; ; New York, : Elsevier, 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos, solitons, and fractals [[e-journal]]
| Chaos, solitons, and fractals [[e-journal]] |
| Pubbl/distr/stampa | [Oxford? ; ; New York?], : Pergamon, 1991- |
| Soggetto topico |
Chaotic behavior in systems
Solitons Fractals |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1873-2887 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
Chaos, solitons and fractals
Chaos, solitons, and fractals Chaos, solitons & fractals |
| Record Nr. | UNINA-9910142682903321 |
| [Oxford? ; ; New York?], : Pergamon, 1991- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaos, solitons, and fractals [[e-journal]]
| Chaos, solitons, and fractals [[e-journal]] |
| Pubbl/distr/stampa | [Oxford? ; ; New York?], : Pergamon, 1991- |
| Soggetto topico |
Chaotic behavior in systems
Solitons Fractals |
| Soggetto genere / forma | Periodicals. |
| ISSN | 1873-2887 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Altri titoli varianti |
Chaos, solitons and fractals
Chaos, solitons, and fractals Chaos, solitons & fractals |
| Record Nr. | UNISA-996204829003316 |
| [Oxford? ; ; New York?], : Pergamon, 1991- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Chaotic dynamics and fractals / / edited by Michael F. Barnsley, Stephen G. Demko
| Chaotic dynamics and fractals / / edited by Michael F. Barnsley, Stephen G. Demko |
| Pubbl/distr/stampa | Orlando, Florida ; ; London, England : , : Academic Press, Inc., , 1986 |
| Descrizione fisica | 1 online resource (305 p.) |
| Disciplina | 515.3/5 |
| Collana | Notes and Reports in Mathematics in Science and Engineering |
| Soggetto topico |
Dynamics
Chaotic behavior in systems Fractals |
| ISBN | 1-4832-6908-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Chaotic Dynamics and Fractals; Copyright Page; Table of Contents; Contributors; Preface; Part I: Chaos and Fractals; CHAPTER 1. CHAOS: SOLVING THE UNSOLVABLE, PREDICTING THE UNPREDICTABLE!; 1. CHAOS: AN ILLUSTRATIVE EXAMPLE; 2. ALGORITHMIC COMPLEXITY THEORY; 3. ALGORITHMIC INTEGRABILITY; 4. ALGORITHMIC RANDOMNESS; 5. QUANTUM CHAOS, IF ANY?; REFERENCES; CHAPTER 2. MAKING CHAOTIC DYNAMICAL SYSTEMS TO ORDER; ABSTRACT; 1. INTRODUCTION; 2. THE COLLAGE THEOREM; 3. MAKING DIFFERENTIAL EQUATIONS WITH PRESCRIBED ATTRACTORS; REFERENCES
CHAPTER 3. ON THE EXISTENCE AND NON-EXISTENCE OF NATURAL BOUNDARIES FOR NON-INTEGRABLE DYNAMICAL SYSTEMSABSTRACT; 1. INTRODUCTION; 2. NONLINEAR DIFFERENTIAL EQUATIONS AND ALGEBRAIC INTEGRABILITY; 3. A CANONICAL EXAMPLE; 4. SOME SIMPLE EXAMPLES; ACKNOWLEDGMENT; REFERENCES; CHAPTER 4. THE HENON MAPPING IN THE COMPLEX DOMAIN; 1. INTRODUCTION; 2. HISTORY AND MOTIVATION; 3. THE RELATION WITH THE THEORY OF POLYNOMIALS; 4. RATES OF ESCAPE FOR THE HENON FAMILY; 5. ANGLES OF ESCAPE; 6. A PROGRAM FOR DESCRIBING MAPPINGS IN THE HENON FAMILY; CHAPTER 5. DYNAMICAL COMPLEXITY OF MAPS OF THE INTERVAL 1. THE ŠARKOVSKII STRATIFICATION2. TOPOLOGICAL ENTROPY; 3. TURBULENCE; 4. ENTROPY MINIMAL ORBITS; 5. HOMOCLINIC ORBITS; ACKNOWLEDGEMENTS; REFERENCES; CHAPTER 6. A USE OF CELLULAR AUTOMATA TO OBTAIN FAMILIES OF FRACTALS; ABSTRACT; 1. A SHORT HISTORY OF CELLULAR AUTOMATA; 2. WHAT ARE CELLULAR AUTOMATA?; 3. RESCALING TO OBTAIN FRACTALS IN THE LIMIT; 4. WAYS OF OBTAINING SOME NUMBERS FROM THE LIMIT SETS; 5. CONCLUSIONS AND DISCUSSION; REFERENCES; Part II: Julia Sets; CHAPTER 7. EXPLODING JULIA SETS; ABSTRACT; 1. INTRODUCTION; 2. AN EXPLOSION IN THE EXPONENTIAL FAMILY CHAPTER 12. DIOPHANTINE PROPERTIES OF JULIA SETS |
| Record Nr. | UNINA-9910786639803321 |
| Orlando, Florida ; ; London, England : , : Academic Press, Inc., , 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Chaotic dynamics and fractals / / edited by Michael F. Barnsley, Stephen G. Demko
| Chaotic dynamics and fractals / / edited by Michael F. Barnsley, Stephen G. Demko |
| Pubbl/distr/stampa | Orlando, Florida ; ; London, England : , : Academic Press, Inc., , 1986 |
| Descrizione fisica | 1 online resource (305 p.) |
| Disciplina | 515.3/5 |
| Collana | Notes and Reports in Mathematics in Science and Engineering |
| Soggetto topico |
Dynamics
Chaotic behavior in systems Fractals |
| ISBN | 1-4832-6908-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Chaotic Dynamics and Fractals; Copyright Page; Table of Contents; Contributors; Preface; Part I: Chaos and Fractals; CHAPTER 1. CHAOS: SOLVING THE UNSOLVABLE, PREDICTING THE UNPREDICTABLE!; 1. CHAOS: AN ILLUSTRATIVE EXAMPLE; 2. ALGORITHMIC COMPLEXITY THEORY; 3. ALGORITHMIC INTEGRABILITY; 4. ALGORITHMIC RANDOMNESS; 5. QUANTUM CHAOS, IF ANY?; REFERENCES; CHAPTER 2. MAKING CHAOTIC DYNAMICAL SYSTEMS TO ORDER; ABSTRACT; 1. INTRODUCTION; 2. THE COLLAGE THEOREM; 3. MAKING DIFFERENTIAL EQUATIONS WITH PRESCRIBED ATTRACTORS; REFERENCES
CHAPTER 3. ON THE EXISTENCE AND NON-EXISTENCE OF NATURAL BOUNDARIES FOR NON-INTEGRABLE DYNAMICAL SYSTEMSABSTRACT; 1. INTRODUCTION; 2. NONLINEAR DIFFERENTIAL EQUATIONS AND ALGEBRAIC INTEGRABILITY; 3. A CANONICAL EXAMPLE; 4. SOME SIMPLE EXAMPLES; ACKNOWLEDGMENT; REFERENCES; CHAPTER 4. THE HENON MAPPING IN THE COMPLEX DOMAIN; 1. INTRODUCTION; 2. HISTORY AND MOTIVATION; 3. THE RELATION WITH THE THEORY OF POLYNOMIALS; 4. RATES OF ESCAPE FOR THE HENON FAMILY; 5. ANGLES OF ESCAPE; 6. A PROGRAM FOR DESCRIBING MAPPINGS IN THE HENON FAMILY; CHAPTER 5. DYNAMICAL COMPLEXITY OF MAPS OF THE INTERVAL 1. THE ŠARKOVSKII STRATIFICATION2. TOPOLOGICAL ENTROPY; 3. TURBULENCE; 4. ENTROPY MINIMAL ORBITS; 5. HOMOCLINIC ORBITS; ACKNOWLEDGEMENTS; REFERENCES; CHAPTER 6. A USE OF CELLULAR AUTOMATA TO OBTAIN FAMILIES OF FRACTALS; ABSTRACT; 1. A SHORT HISTORY OF CELLULAR AUTOMATA; 2. WHAT ARE CELLULAR AUTOMATA?; 3. RESCALING TO OBTAIN FRACTALS IN THE LIMIT; 4. WAYS OF OBTAINING SOME NUMBERS FROM THE LIMIT SETS; 5. CONCLUSIONS AND DISCUSSION; REFERENCES; Part II: Julia Sets; CHAPTER 7. EXPLODING JULIA SETS; ABSTRACT; 1. INTRODUCTION; 2. AN EXPLOSION IN THE EXPONENTIAL FAMILY CHAPTER 12. DIOPHANTINE PROPERTIES OF JULIA SETS |
| Record Nr. | UNINA-9910829150503321 |
| Orlando, Florida ; ; London, England : , : Academic Press, Inc., , 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Fractals
(181)
- Chaotic behavior in systems (31)
- Dynamics (9)
- Wavelets (Mathematics) (9)
- Stochastic processes (7)