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Fractal geometry : mathematical foundations and applications / / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / / Kenneth Falconer |
| Autore | Falconer K. J. <1952-> |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken : , : John Wiley & Sons, , 2014 |
| Descrizione fisica | 1 online resource (400 p.) |
| Disciplina | 514/.742 |
| Soggetto topico |
Fractals
Dimension theory (Topology) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-76286-X
1-118-76285-1 |
| Classificazione | MAT031000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Contents; Preface to the first edition; Preface to the second edition; Preface to the third edition; Course suggestions; Introduction; Part I Foundations; Chapter 1 Mathematical background; 1.1 Basic set theory; 1.2 Functions and limits; 1.3 Measures and mass distributions; 1.4 Notes on probability theory; 1.5 Notes and references; Exercises; Chapter 2 Box-counting dimension; 2.1 Box-counting dimensions; 2.2 Properties and problems of box-counting dimension; 2.3 Modified box-counting dimensions; 2.4 Some other definitions of dimension; 2.5 Notes and references
ExercisesChapter 3 Hausdorff and packing measures and dimensions; 3.1 Hausdorff measure; 3.2 Hausdorff dimension; 3.3 Calculation of Hausdorff dimension-simple examples; 3.4 Equivalent definitions of Hausdorff dimension; 3.5 Packing measure and dimensions; 3.6 Finer definitions of dimension; 3.7 Dimension prints; 3.8 Porosity; 3.9 Notes and references; Exercises; Chapter 4 Techniques for calculating dimensions; 4.1 Basic methods; 4.2 Subsets of finite measure; 4.3 Potential theoretic methods; 4.4 Fourier transform methods; 4.5 Notes and references; Exercises Chapter 5 Local structure of fractals5.1 Densities; 5.2 Structure of 1-sets; 5.3 Tangents to s-sets; 5.4 Notes and references; Exercises; Chapter 6 Projections of fractals; 6.1 Projections of arbitrary sets; 6.2 Projections of s-sets of integral dimension; 6.3 Projections of arbitrary sets of integral dimension; 6.4 Notes and references; Exercises; Chapter 7 Products of fractals; 7.1 Product formulae; 7.2 Notes and references; Exercises; Chapter 8 Intersections of fractals; 8.1 Intersection formulae for fractals; 8.2 Sets with large intersection; 8.3 Notes and references; Exercises Part II Applications and ExamplesChapter 9 Iterated function systems-self-similar and self-affine sets; 9.1 Iterated function systems; 9.2 Dimensions of self-similar sets; 9.3 Some variations; 9.4 Self-affine sets; 9.5 Applications to encoding images; 9.6 Zeta functions and complex dimensions; 9.7 Notes and references; Exercises; Chapter 10 Examples from number theory; 10.1 Distribution of digits of numbers; 10.2 Continued fractions; 10.3 Diophantine approximation; 10.4 Notes and references; Exercises; Chapter 11 Graphs of functions; 11.1 Dimensions of graphs 11.2 Autocorrelation of fractal functions11.3 Notes and references; Exercises; Chapter 12 Examples from pure mathematics; 12.1 Duality and the Kakeya problem; 12.2 Vitushkin's conjecture; 12.3 Convex functions; 12.4 Fractal groups and rings; 12.5 Notes and references; Exercises; Chapter 13 Dynamical systems; 13.1 Repellers and iterated function systems; 13.2 The logistic map; 13.3 Stretching and folding transformations; 13.4 The solenoid; 13.5 Continuous dynamical systems; 13.6 Small divisor theory; 13.7 Lyapunov exponents and entropies; 13.8 Notes and references; Exercises Chapter 14 Iteration of complex functions-Julia sets and the Mandelbrot set |
| Record Nr. | UNINA-9910453807903321 |
Falconer K. J. <1952->
|
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| Hoboken : , : John Wiley & Sons, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry : mathematical foundations and applications / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / Kenneth Falconer |
| Autore | Falconer, Kenneth |
| Edizione | [3. ed.] |
| Pubbl/distr/stampa | Chichester, : Wiley, 2014 |
| Descrizione fisica | xxx, 368 p. : ill. ; 23 cm |
| Disciplina |
516.15
512.5-FAL-1A |
| Soggetto non controllato |
Geometria algebrica
Topologia Topologia algebrica Sistemi dinamici Frattali matematici |
| ISBN | 978-1-119-94239-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910629699403321 |
|
Falconer, Kenneth
|
||
| Chichester, : Wiley, 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal Geometry : Mathematical Foundations and Applications
| Fractal Geometry : Mathematical Foundations and Applications |
| Autore | Falconer Kenneth |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | New York : , : John Wiley & Sons, Incorporated, , 2014 |
| Descrizione fisica | 1 online resource (400 pages) |
| Disciplina | 514/.742 |
| Altri autori (Persone) | FalconerKenneth |
| Soggetto topico |
Fractals
Dimension theory (Topology) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9781118762851
9781119942399 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- Preface to the first edition -- Preface to the second edition -- Preface to the third edition -- Course suggestions -- Introduction -- Part I Foundations -- Chapter 1 Mathematical background -- 1.1 Basic set theory -- 1.2 Functions and limits -- 1.3 Measures and mass distributions -- 1.4 Notes on probability theory -- 1.5 Notes and references -- Exercises -- Chapter 2 Box-counting dimension -- 2.1 Box-counting dimensions -- 2.2 Properties and problems of box-counting dimension -- 2.3 Modified box-counting dimensions -- 2.4 Some other definitions of dimension -- 2.5 Notes and references -- Exercises -- Chapter 3 Hausdorff and packing measures and dimensions -- 3.1 Hausdorff measure -- 3.2 Hausdorff dimension -- 3.3 Calculation of Hausdorff dimension-simple examples -- 3.4 Equivalent definitions of Hausdorff dimension -- 3.5 Packing measure and dimensions -- 3.6 Finer definitions of dimension -- 3.7 Dimension prints -- 3.8 Porosity -- 3.9 Notes and references -- Exercises -- Chapter 4 Techniques for calculating dimensions -- 4.1 Basic methods -- 4.2 Subsets of finite measure -- 4.3 Potential theoretic methods -- 4.4 Fourier transform methods -- 4.5 Notes and references -- Exercises -- Chapter 5 Local structure of fractals -- 5.1 Densities -- 5.2 Structure of 1-sets -- 5.3 Tangents to s-sets -- 5.4 Notes and references -- Exercises -- Chapter 6 Projections of fractals -- 6.1 Projections of arbitrary sets -- 6.2 Projections of s-sets of integral dimension -- 6.3 Projections of arbitrary sets of integral dimension -- 6.4 Notes and references -- Exercises -- Chapter 7 Products of fractals -- 7.1 Product formulae -- 7.2 Notes and references -- Exercises -- Chapter 8 Intersections of fractals -- 8.1 Intersection formulae for fractals -- 8.2 Sets with large intersection -- 8.3 Notes and references.
Exercises -- Part II Applications and Examples -- Chapter 9 Iterated function systems-self-similar and self-affine sets -- 9.1 Iterated function systems -- 9.2 Dimensions of self-similar sets -- 9.3 Some variations -- 9.4 Self-affine sets -- 9.5 Applications to encoding images -- 9.6 Zeta functions and complex dimensions -- 9.7 Notes and references -- Exercises -- Chapter 10 Examples from number theory -- 10.1 Distribution of digits of numbers -- 10.2 Continued fractions -- 10.3 Diophantine approximation -- 10.4 Notes and references -- Exercises -- Chapter 11 Graphs of functions -- 11.1 Dimensions of graphs -- 11.2 Autocorrelation of fractal functions -- 11.3 Notes and references -- Exercises -- Chapter 12 Examples from pure mathematics -- 12.1 Duality and the Kakeya problem -- 12.2 Vitushkin's conjecture -- 12.3 Convex functions -- 12.4 Fractal groups and rings -- 12.5 Notes and references -- Exercises -- Chapter 13 Dynamical systems -- 13.1 Repellers and iterated function systems -- 13.2 The logistic map -- 13.3 Stretching and folding transformations -- 13.4 The solenoid -- 13.5 Continuous dynamical systems -- 13.6 Small divisor theory -- 13.7 Lyapunov exponents and entropies -- 13.8 Notes and references -- Exercises -- Chapter 14 Iteration of complex functions-Julia sets and the Mandelbrot set -- 14.1 General theory of Julia sets -- 14.2 Quadratic functions-the Mandelbrot set -- 14.3 Julia sets of quadratic functions -- 14.4 Characterisation of quasi-circles by dimension -- 14.5 Newton's method for solving polynomial equations -- 14.6 Notes and references -- Exercises -- Chapter 15 Random fractals -- 15.1 A random Cantor set -- 15.2 Fractal percolation -- 15.3 Notes and references -- Exercises -- Chapter 16 Brownian motion and Brownian surfaces -- 16.1 Brownian motion in R -- 16.2 Brownian motion in Rn -- 16.3 Fractional Brownian motion. 16.4 Fractional Brownian surfaces -- 16.5 Lévy stable processes -- 16.6 Notes and references -- Exercises -- Chapter 17 Multifractal measures -- 17.1 Coarse multifractal analysis -- 17.2 Fine multifractal analysis -- 17.3 Self-similar multifractals -- 17.4 Notes and references -- Exercises -- Chapter 18 Physical applications -- 18.1 Fractal fingering -- 18.2 Singularities of electrostatic and gravitational potentials -- 18.3 Fluid dynamics and turbulence -- 18.4 Fractal antennas -- 18.5 Fractals in finance -- 18.6 Notes and references -- Exercises -- References -- Index. |
| Record Nr. | UNINA-9910795832003321 |
|
Falconer Kenneth
|
||
| New York : , : John Wiley & Sons, Incorporated, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry : mathematical foundations and applications / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / Kenneth Falconer |
| Autore | Falconer, Kenneth J. |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Chichester [etc.], : Wiley, 2003 |
| Descrizione fisica | XXVII,337 p. : ill. ; 23 cm |
| Disciplina | 514.742 |
| Soggetto non controllato | Frattali |
| ISBN | 978-0-470-84862-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990003996570403321 |
|
Falconer, Kenneth J.
|
||
| Chichester [etc.], : Wiley, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fractal geometry / Kenneth Falconer
| Fractal geometry / Kenneth Falconer |
| Autore | Falconer, Kenneth J. |
| Edizione | [Repr. with corr] |
| Pubbl/distr/stampa | Chichester, : Wiley, 1997 |
| Descrizione fisica | XXII, 288 p. : ill. ; 24 cm. |
| Soggetto topico |
28-XX - Measure and integration [MSC 2020]
28A80 - Fractals [MSC 2020] 28A75 - Length, area, volume, other geometric measure theory [MSC 2020] 37C70 - Attractors and repellers of smooth dynamical systems and their topological structure [MSC 2020] |
| ISBN |
04-7196-777-7
978-04-7196-777-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-SUN0055860 |
|
Falconer, Kenneth J.
|
||
| Chichester, : Wiley, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Fractal geometry / Kenneth Falconer
| Fractal geometry / Kenneth Falconer |
| Autore | Falconer, Kenneth J. |
| Edizione | [Repr. with corr] |
| Pubbl/distr/stampa | Chichester, : Wiley, 1997 |
| Descrizione fisica | XXII, 288 p. : ill. ; 24 cm |
| Soggetto topico |
28-XX - Measure and integration [MSC 2020]
28A80 - Fractals [MSC 2020] 28A75 - Length, area, volume, other geometric measure theory [MSC 2020] 37C70 - Attractors and repellers of smooth dynamical systems and their topological structure [MSC 2020] |
| ISBN |
04-7196-777-7
978-04-7196-777-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0055860 |
|
Falconer, Kenneth J.
|
||
| Chichester, : Wiley, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Fractal geometry / Kenneth Falconer
| Fractal geometry / Kenneth Falconer |
| Autore | Falconer, Kenneth J. |
| Edizione | [Repr. with corr] |
| Pubbl/distr/stampa | Chichester, : Wiley, 1997 |
| Descrizione fisica | XXII, 288 p. : ill. ; 24 cm |
| Soggetto topico |
28-XX - Measure and integration [MSC 2020]
28A75 - Length, area, volume, other geometric measure theory [MSC 2020] 28A80 - Fractals [MSC 2020] 37C70 - Attractors and repellers of smooth dynamical systems and their topological structure [MSC 2020] |
| ISBN |
04-7196-777-7
978-04-7196-777-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00055860 |
|
Falconer, Kenneth J.
|
||
| Chichester, : Wiley, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Fractal geometry : mathematical foundation and applications / Kenneth Falconer
| Fractal geometry : mathematical foundation and applications / Kenneth Falconer |
| Autore | Falconer, Kenneth |
| Pubbl/distr/stampa |
< |
| Descrizione fisica | XXII, 288 p. : ill. ; 24 cm. |
| Disciplina | 514.74 |
| Soggetto topico | Frattali |
| ISBN | 0-471-92287-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNIBAS-000011684 |
|
Falconer, Kenneth
|
||
| <<John>> Wiley | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. della Basilicata | ||
| ||
Fractal geometry : mathematical foundations and applications / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / Kenneth Falconer |
| Autore | Falconer, Kenneth |
| Pubbl/distr/stampa | Chichester [etc.] : John Wiley & Sons, copyr. 1990 |
| Descrizione fisica | XXII, 288 p. : ill. ; 23 cm |
| Disciplina | 5169 |
| Soggetto non controllato | frattali |
| ISBN | 0-471-92287-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-990000252650203316 |
|
Falconer, Kenneth
|
||
| Chichester [etc.] : John Wiley & Sons, copyr. 1990 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Fractal geometry : mathematical foundations and applications / Kenneth Falconer
| Fractal geometry : mathematical foundations and applications / Kenneth Falconer |
| Autore | Falconer, Kenneth |
| Pubbl/distr/stampa | Chichester [etc.] : John Wiley & Sons, copyr. 1990 |
| Descrizione fisica | XXII, 288 p. : ill. ; 23 cm |
| Disciplina | 5169 |
| Soggetto non controllato | frattali |
| ISBN | 0-471-92287-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-990000152540203316 |
|
Falconer, Kenneth
|
||
| Chichester [etc.] : John Wiley & Sons, copyr. 1990 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
