Open conformal systems and perturbations of transfer operators / Mark Pollicott, Mariusz Urbański.

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Open conformal systems and perturbations of transfer operators / Mark Pollicott, Mariusz Urbański.

9783319721798 (electronic book)
3319721798 (electronic book)
9783319721781

Cham, Switzerland : Springer, 2017.

English

1 online resource (xii, 204 pages).

10.1007/978-3-319-72179-8 doi

QA609

516.3/5

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed February 13, 2018).

Lecture notes in mathematics (Springer-Verlag) ; 2206.

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