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Open Conformal Systems and Perturbations of Transfer Operators
Af: Mark Pollicott, Mariusz Urbanski Engelsk Paperback
SPAR
kr 191
Open Conformal Systems and Perturbations of Transfer Operators
Af: Mark Pollicott, Mariusz Urbanski Engelsk Paperback

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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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.

Produktdetaljer
Sprog: Engelsk
Sider: 204
ISBN-13: 9783319721781
Indbinding: Paperback
Udgave:
ISBN-10: 331972178X
Udg. Dato: 7 feb 2018
Længde: 17mm
Bredde: 236mm
Højde: 156mm
Oplagsdato: 7 feb 2018
Forfatter(e) Mark Pollicott, Mariusz Urbanski


Kategori Kompleks analyse, komplekse variabler


Sprog Engelsk


Indbinding Paperback


Sider 204


Udgave


Længde 17mm


Bredde 236mm


Højde 156mm

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