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Conformal fractals : = ergodic theor...

Przytycki, Feliks.

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Conformal fractals : = ergodic theory methods /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Conformal fractals :/ Feliks Przytycki, Mariusz Urbanski.
其他題名:	ergodic theory methods /
作者:	Przytycki, Feliks.
其他作者:	Urbanski, Mariusz.
出版者:	Cambridge ;Cambridge University Press, : 2010.,
面頁冊數:	x, 354 p. :ill. ;23 cm.
內容註:	Introduction -- 1. Basic examples and definitions 2. Measure-preserving endomorphisms -- 3. Ergodic theory on compact metric spaces -- 4. Distance-expanding maps -- 5. Thermodynamical formalism -- 6. Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- 7. Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- 8. Fractal dimensions -- 9. Conformal expanding repellers -- 10. Sullivan's classification of conformal expanding repellers -- 11. Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- 12. Conformal measures.
標題:	Conformal geometry. -
ISBN:	9780521438001 (pbk.) :

Conformal fractals : = ergodic theory methods /
Przytycki, Feliks.

Conformal fractals :ergodic theory methods /Feliks Przytycki, Mariusz Urbanski. - Cambridge ;Cambridge University Press,2010. - x, 354 p. :ill. ;23 cm. - London Mathematical Society lecture note series ;371. - London Mathematical Society lecture note series ;359..

Includes bibliographical references (p. 336-348) and index.

Introduction -- 1. Basic examples and definitions 2. Measure-preserving endomorphisms -- 3. Ergodic theory on compact metric spaces -- 4. Distance-expanding maps -- 5. Thermodynamical formalism -- 6. Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- 7. Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- 8. Fractal dimensions -- 9. Conformal expanding repellers -- 10. Sullivan's classification of conformal expanding repellers -- 11. Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- 12. Conformal measures.

"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"--Provided by publisher.

ISBN: 9780521438001 (pbk.) :US77.99

LCCN: 2009054019

Nat. Bib. No.: GBB004238bnb

Nat. Bib. Agency Control No.: 015462058UkSubjects--Topical Terms:

708569
Conformal geometry.

LC Class. No.: QA609 / .P79 2010

Dewey Class. No.: 514/.742

Conformal fractals : = ergodic theory methods /
LDR:02433cam 2200265 a 4500 001 975148
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005 20100903122148.0
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015 $a GBB004238 $2 bnb
016 7 $a 015462058 $2 Uk
020 $a 9780521438001 (pbk.) : $c US77.99
020 $a 0521438004 (pbk.)
035 $a (OCoLC)ocn460059767
035 $a AS-BW-100-N-01
040 $a DLC $c DLC $d UKM $d BTCTA $d BWKUK $d BWK $d CDX $d YDXCP $d BWX $d IAY $d DLC
050 0 0 $a QA609 $b .P79 2010
082 0 0 $a 514/.742 $2 22
100 1 $a Przytycki, Feliks. $3 1299069
245 1 0 $a Conformal fractals : $b ergodic theory methods / $c Feliks Przytycki, Mariusz Urbanski.
260 # $a Cambridge ; $a New York : $b Cambridge University Press, $c 2010.
300 $a x, 354 p. : $b ill. ; $c 23 cm.
490 1 $a London Mathematical Society lecture note series ; $v 371
504 $a Includes bibliographical references (p. 336-348) and index.
505 0 # $a Introduction -- 1. Basic examples and definitions 2. Measure-preserving endomorphisms -- 3. Ergodic theory on compact metric spaces -- 4. Distance-expanding maps -- 5. Thermodynamical formalism -- 6. Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- 7. Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- 8. Fractal dimensions -- 9. Conformal expanding repellers -- 10. Sullivan's classification of conformal expanding repellers -- 11. Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- 12. Conformal measures.
520 # $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"--Provided by publisher.
650 # 0 $a Conformal geometry. $3 708569
650 # 0 $a Fractals. $3 524457
650 # 0 $a Ergodic theory. $3 555691
650 # 0 $a Iterative methods (Mathematics) $3 648278
700 1 # $a Urbanski, Mariusz. $3 752945
830 0 $a London Mathematical Society lecture note series ; $v 359. $3 1232938