Overview
- Contains entirely original results which cannot be found elsewhere in the literature
- Treats topics which are now the subject of rapidly developing extensive research
- Serves both as a reference and as a source of inspiration for further original work
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2206)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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, rational functions and meromorphic maps.
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.
Authors and Affiliations
Bibliographic Information
Book Title: Open Conformal Systems and Perturbations of Transfer Operators
Authors: Mark Pollicott, Mariusz Urbański
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-72179-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-72178-1Published: 07 February 2018
eBook ISBN: 978-3-319-72179-8Published: 05 February 2018
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 204
Topics: Dynamical Systems and Ergodic Theory, Functional Analysis, Functions of a Complex Variable, Operator Theory, Measure and Integration