---

＜電子ブック＞
Open Conformal Systems and Perturbations of Transfer Operators / by Mark Pollicott, Mariusz Urbański
(Lecture Notes in Mathematics. ISSN:16179692 ; 2206)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	XII, 204 p : online resource
著者標目	*Pollicott, Mark author Urbański, Mariusz author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Functional analysis LCSH:Functions of complex variables LCSH:Operator theory LCSH:Measure theory FREE:Dynamical Systems FREE:Functional Analysis FREE:Functions of a Complex Variable FREE:Operator Theory FREE:Measure and Integration
一般注記	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 Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets HTTP:URL=https://doi.org/10.1007/978-3-319-72179-8

 類似資料