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Open conformal systems and perturbat...

Pollicott, Mark,

Open conformal systems and perturbations of transfer operators

Record Type:	Electronic resources : Monograph/item
Title/Author:	Open conformal systems and perturbations of transfer operatorsby Mark Pollicott, Mariusz Urbanski.
Author:	Pollicott, Mark,
other author:	Urbanski, Mariusz,
Published:	Cham :Springer International Publishing :2017.
Description:	xii, 204 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Conformal geometry.
Online resource:	http://dx.doi.org/10.1007/978-3-319-72179-8
ISBN:	9783319721798$q(electronic bk.)

Open conformal systems and perturbations of transfer operators
Pollicott, Mark,

Open conformal systems and perturbations of transfer operators[electronic resource] /by Mark Pollicott, Mariusz Urbanski. - Cham :Springer International Publishing :2017. - xii, 204 p. :ill., digital ;24 cm. - Lecture notes in mathematics,22060075-8434 ;. - Lecture notes in mathematics ;2035..

1. Introduction -- 2. Singular Perturbations of Classical Original Perron-Frobenius Operators on Countable Alphabet Symbol Spaces -- 3. Symbol Escape Rates and the Survivor Set K(Un) -- 4. Escape Rates for Conformal GDMSs and IFSs -- 5. Applications: Escape Rates for Multimodal Maps and One-Dimensional Complex Dynamics.

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, meromorphic maps and rational functions. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Holder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.

ISBN: 9783319721798$q(electronic bk.)

Standard No.: 10.1007/978-3-319-72179-8doiSubjects--Topical Terms:

468280
Conformal geometry.

LC Class. No.: QA609

Dewey Class. No.: 516.35

Open conformal systems and perturbations of transfer operators
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245 1 0 $a Open conformal systems and perturbations of transfer operators $h [electronic resource] / $c by Mark Pollicott, Mariusz Urbanski.
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300 $a xii, 204 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2206
505 0 $a 1. Introduction -- 2. Singular Perturbations of Classical Original Perron-Frobenius Operators on Countable Alphabet Symbol Spaces -- 3. Symbol Escape Rates and the Survivor Set K(Un) -- 4. Escape Rates for Conformal GDMSs and IFSs -- 5. Applications: Escape Rates for Multimodal Maps and One-Dimensional Complex Dynamics.
520 $a The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, meromorphic maps and rational functions. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Holder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.
650 0 $a Conformal geometry. $3 468280
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650 2 4 $a Functional Analysis. $3 274845
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650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Measure and Integration. $3 273777
700 1 $a Urbanski, Mariusz, $e author. $3 798627
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