DEVIATION OF ERGODIC AVERAGES FOR SUBSTITUTION DYNAMICAL SYSTEMS WITH EIGENVALUES OF MODULUS ONEReport as inadecuate




DEVIATION OF ERGODIC AVERAGES FOR SUBSTITUTION DYNAMICAL SYSTEMS WITH EIGENVALUES OF MODULUS ONE - Download this document for free, or read online. Document in PDF available to download.

1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 I2M - Institut de Mathématiques de Marseille 3 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of mod-ulus 1. The functions γ we consider are the corresponding eigen-functions. In Theorem 1.1 we prove that the limit inferior of the ergodic sums n, γx 0 +.

+ γx n−1 n∈N is bounded for every point x in the phase space. In Theorem 1.2, we prove existence of limit distributions along certain exponential subsequences of times for substitutions of constant length. Under additional assumptions, we prove that ergodic integrals satisfy the Central Limit Theorem Theorem 1.3, Theorem 1.9.





Author: Xavier Bressaud - Alexander I. Bufetov - Pascal Hubert -

Source: https://hal.archives-ouvertes.fr/



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