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Open conformal systems and perturbat...

Pollicott, Mark,

Open conformal systems and perturbations of transfer operators

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Open conformal systems and perturbations of transfer operatorsby Mark Pollicott, Mariusz Urbanski.
作者:	Pollicott, Mark,
其他作者:	Urbanski, Mariusz,
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xii, 204 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Conformal geometry.
電子資源:	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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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.
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