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Asymptotic Formula for Counting in Deterministic and Random Dynamical Systems

The lattice point problem in dynamical systems investigates the distribution of certain objects with some length property in the space that the dynamics is defined. This problem in different contexts can be interpreted differently. In the context of symbolic dynamical systems, we are trying to investigate the growth of N(T), the number of finite words subject to a specific ergodic length T, as T tends to infinity. This problem has been investigated by Pollicott and Urbański to a great extent. We try to investigate it further, by relaxing a condition in the context of deterministic dynamical systems. Moreover, we investigate this problem in the context of random dynamical systems. The method for us is considering the Fourier-Stieltjes transform of N(T) and expressing it via a Poincaré series for which the spectral gap property of the transfer operator, enables us to apply some appropriate Tauberian theorems to understand asymptotic growth of N(T). For counting in the random dynamics, we use some results from probability theory.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc2137552
Date05 1900
CreatorsNaderiyan, Hamid
ContributorsUrbański, Mariusz, Cherry, William, Fishman, Lior
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsPublic, Naderiyan, Hamid, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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