Fractal Geometry Mathematical Foundations and Applications.

Detalles Bibliográficos
Autor principal: Falconer, Kenneth
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

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