國立高雄大學圖資館 |

Language: English

Back

Ergodic theory of expanding Thurston...

Li, Zhiqiang.

Ergodic theory of expanding Thurston maps

Record Type:	Electronic resources : Monograph/item
Title/Author:	Ergodic theory of expanding Thurston mapsby Zhiqiang Li.
Author:	Li, Zhiqiang.
Published:	Paris :Atlantis Press :2017.
Description:	xii, 182 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Ergodic theory.
Online resource:	http://dx.doi.org/10.2991/978-94-6239-174-1
ISBN:	9789462391741$q(electronic bk.)

Ergodic theory of expanding Thurston maps
Li, Zhiqiang.

Ergodic theory of expanding Thurston maps[electronic resource] /by Zhiqiang Li. - Paris :Atlantis Press :2017. - xii, 182 p. :ill., digital ;24 cm. - Atlantis studies in dynamical systems ;v.4. - Atlantis studies in dynamical systems ;v.1..

1.Introduction -- 2.Thurston maps -- 3.Ergodic theory -- 4.The measure of maximal entropy -- 5.Equilibrium states -- 6.Asymptotic h-Expansiveness -- 7.Large deviation principles.

Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.

ISBN: 9789462391741$q(electronic bk.)

Standard No.: 10.2991/978-94-6239-174-1doiSubjects--Topical Terms:

219112
Ergodic theory.

LC Class. No.: QA313

Dewey Class. No.: 515.48

Ergodic theory of expanding Thurston maps
LDR:02284nmm a2200325 a 4500 001 512205
003 DE-He213
005 20170406110453.0
006 m d
007 cr nn 008maaau
008 171226s2017 fr s 0 eng d
020 $a 9789462391741$q(electronic bk.)
020 $a 9789462391734$q(paper)
024 7 $a 10.2991/978-94-6239-174-1 $2 doi
035 $a 978-94-6239-174-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA313
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.48 $2 23
090 $a QA313 $b .L693 2017
100 1 $a Li, Zhiqiang. $3 509813
245 1 0 $a Ergodic theory of expanding Thurston maps $h [electronic resource] / $c by Zhiqiang Li.
260 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2017.
300 $a xii, 182 p. : $b ill., digital ; $c 24 cm.
490 1 $a Atlantis studies in dynamical systems ; $v v.4
505 0 $a 1.Introduction -- 2.Thurston maps -- 3.Ergodic theory -- 4.The measure of maximal entropy -- 5.Equilibrium states -- 6.Asymptotic h-Expansiveness -- 7.Large deviation principles.
520 $a Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.
650 0 $a Ergodic theory. $3 219112
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Functions of a Complex Variable. $3 275780
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Atlantis studies in dynamical systems ; $v v.1. $3 573185
856 4 0 $u http://dx.doi.org/10.2991/978-94-6239-174-1
950 $a Mathematics and Statistics (Springer-11649)