Conformal fractals : ergodic theory methods / Feliks Przytycki, Mariusz Urbański.

Call Number	514/.742
Author	Przytycki, Feliks, author.
Title	Conformal fractals : ergodic theory methods / Feliks Przytycki, Mariusz Urbański.
Physical Description	1 online resource (x, 354 pages) : digital, PDF file(s).
Series	London Mathematical Society lecture note series ; 371
Notes	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Contents	Introduction -- Basic examples and definitions -- Ergodic theory on compact metric spaces -- Distance-expanding maps -- Thermodynamical formalism -- Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- Fractal dimensions -- Conformal expanding repellers -- Sullivan's classification of conformal expanding repellers -- Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- Conformal measures.
Summary	This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.
Added Author	Urbański, Mariusz, author.
Subject	Conformal geometry. FRACTALS. ERGODIC THEORY. Iterative methods (Mathematics)
Multimedia	https://doi.org/10.1017/CBO9781139193184

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$t Introduction -- $g 1. $t Basic examples and definitions -- $g 2. Measure-preserving endomorphisms -- $g 3. $t Ergodic theory on compact metric spaces -- $g 4. $t Distance-expanding maps -- $g 5. $t Thermodynamical formalism -- $g 6. $t Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- $g 7. $t Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- $g 8. $t Fractal dimensions -- $g 9. $t Conformal expanding repellers -- $g 10. $t Sullivan's classification of conformal expanding repellers -- $g 11. $t Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- $g 12. $t Conformal measures.

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$a This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.

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$a Conformal geometry.

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$a FRACTALS.

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$a ERGODIC THEORY.

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$a Iterative methods (Mathematics)

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$a London Mathematical Society lecture note series ; $v 371.

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Summary	This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.
Notes	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Contents	Introduction -- Basic examples and definitions -- Ergodic theory on compact metric spaces -- Distance-expanding maps -- Thermodynamical formalism -- Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- Fractal dimensions -- Conformal expanding repellers -- Sullivan's classification of conformal expanding repellers -- Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- Conformal measures.
Subject	Conformal geometry. FRACTALS. ERGODIC THEORY. Iterative methods (Mathematics)
Multimedia	https://doi.org/10.1017/CBO9781139193184