1.

Record Nr.

UNINA9910829150503321

Titolo

Chaotic dynamics and fractals / / edited by Michael F. Barnsley, Stephen G. Demko

Pubbl/distr/stampa

Orlando, Florida ; ; London, England : , : Academic Press, Inc., , 1986

©1986

ISBN

1-4832-6908-6

Descrizione fisica

1 online resource (305 p.)

Collana

Notes and Reports in Mathematics in Science and Engineering ; ; Volume 2

Disciplina

515.3/5

Soggetti

Dynamics

Chaotic behavior in systems

Fractals

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references at the end of each chapters.

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

Sommario/riassunto

Chaotic Dynamics and Fractals