This section contains free e-books and guides on Fractals, some of the resources in this section can be viewed online and some of them can be downloaded.
A tale of two fractalsA. A. KirillovPDF
| 134 Pages
This book is devoted to a phenomenon of
fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket,
Harmonic functions on Sierpinski gasket, Applications of generalized numerical
systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets,
Geometric and group-theoretic approach.
Lectures on fractal geometry and dynamicsMichael HochmanPDF
| 96 Pages
Goal of this course
note is primarily to develop the foundations of geometric measure theory, and
covers in detail a variety of classical subjects. A secondary goal is to
demonstrate some applications and interactions with dynamics and metric number
Lecture Notes On Dynamical Systems, chaos and Fractal GeometryGeoffrey R.
| 258 Pages
The first 12 chapters cover fairly standard topics in one dimensional
dynamics and should be accessible to most upper level undergraduate students.
The requirements from real analysis and topology are developed as the
material progresses. Chapter 13 gives an introduction to the theory of substitutions and shows how these can give rise to certain types
of fractals. Subsequent chapters develop the rigorous mathematical theory of
substitutions and Sturmian sequences.
Lectures On Fractals And Dimension TheoryMark PollicottPDF
| 106 Pages
This note covers the
following topics: Basic Properties and Examples, Iterated Function Schemes,
Computing dimension, Some Number Theory and algorithms, Measures and Dimension,
Classic results: Projections, Slices and translations, Tranversality and
Iterated function schemes with overlaps.
Fractals in the Plane the Ergodic Theory MethodsFeliks Przytycki
| 324 Pages
This book is an introduction to the theory of iteration of
expanding and nonuniformly expanding holomorphic maps and topics in geometric
measure theory of the underlying invariant fractal sets. Major topics covered:
Basic examples and definitions, Measure preserving endomorphisms, Ergodic theory
on compact metric spaces, Distance expanding maps, Thermodynamical formalism,
Expanding repellers in manifolds and Riemann sphere, preliminaries, Cantor
repellers in the line, Sullivanís scaling function, application in Feigenbaum
universality, Fractal dimensions, Sullivanís classification of conformal
expanding repellers, Conformal maps with invariant probability measures of
positive, Lyapunov exponent and Conformal measures.
Conformal DynamicsCurtis T McMullenOnline
| NA Pages
This note covers the following topics: Rigidity and inflexibility in conformal dynamics, Hausdorff
dimension and conformal dynamics: Strong convergence of Kleinian groups,
Geometrically finite rational maps and Computation of dimension.
Chaos, Fractals, and ArcadiaRobert
| NA Pages
This note covers the following topics: Thomasina's Geometry of
Irregular Forms, The Chaos Game, The Sierpinski Hexagon, Thomasina's Fern
and Valentine's Grouse.
|Chaos and Fractals New Frontiers of Sciences|
|The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs|
|The Fractal Geometry of the Mandelbrot Set, How to Count and How to Add|
|Fractals A Fractals Lesson for Elementary and Middle School Students|
|Lecture Notes on Fractal Geometry|