Asymptotic Counting in Conformal Dynamical Systems - Couverture souple

Pollicott, Mark; Urbanski, Mariusz

 
9781470465773: Asymptotic Counting in Conformal Dynamical Systems
Couverture souple
ISBN 10 : 1470465779 ISBN 13 : 9781470465773
Editeur : American Mathematical Society, 2021

Synopsis

"In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former. We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights. These results have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps,continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups, and many more. This gives a unified approach which both recovers known results and proves new results. Our new approach is founded on spectral properties of complexified Ruelle- Perron-Frobenius operators and Tauberian theorems as used in classical problems of prime number theory"--

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Mark Pollicott, University of Warwick, Coventry, United Kingdom.

Mariusz Urbanski, University of North Texas, Denton, TX.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2021
Langue
anglais
ISBN 10 
1470465779
ISBN 13 
9781470465773
Reliure
Broché
Nombre de pages
139
Coordonnées du fabricant
non disponible
Personne responsable
non disponible