Open Conformal Systems and Perturbations of Transfer Operators

Released on by Mark Pollicott
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  • Open Conformal Systems and Perturbations of Transfer Operators Book Detail

  • Author : Mark Pollicott
  • Release Date : 2018-02-05
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 207
  • ISBN 13 : 3319721798
  • File Size : 72,72 MB
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Open Conformal Systems and Perturbations of Transfer Operators by Mark Pollicott PDF Summary

Book Description: 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.

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Open Quantum Systems II

Open Quantum Systems II

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Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental