Mathematics Books Fractals Books

A tale of two fractals

A tale of two fractals

A tale of two fractals

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.

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s134 Pages
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A tale of two fractals

A tale of two fractals

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.

s134 Pages
Lectures on fractal geometry and dynamics

Lectures on fractal geometry and dynamics

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 theory.

s96 Pages
Lectures On Fractals And Dimension Theory

Lectures On Fractals And Dimension Theory

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.

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Fractals in the Plane   the Ergodic Theory Methods

Fractals in the Plane the Ergodic Theory Methods

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.

s324 Pages
Chaos, Fractals, and Arcadia

Chaos, Fractals, and Arcadia

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.

sNA Pages
Chaos               and Fractals New Frontiers of Sciences

Chaos and Fractals New Frontiers of Sciences

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The Fractal Geometry of the       Mandelbrot Set, The Periods of the Bulbs

The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs

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Fractals   A Fractals Lesson       for Elementary and Middle School Students

Fractals A Fractals Lesson for Elementary and Middle School Students

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