Lecture Notes in Mathematics

Open Conformal Systems and Perturbations of Transfer Operators

Authors: Pollicott, Mark, Urbański, Mariusz

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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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-72179-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-72178-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Open Conformal Systems and Perturbations of Transfer Operators
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2206
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-72179-8
DOI
10.1007/978-3-319-72179-8
Softcover ISBN
978-3-319-72178-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 204
Topics