Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus one

Details Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus one Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus one

2011-06-14

arxiv.org/abs/1106.2666v1

Mathematics

Dynamical Systems

49 pages, 5 figures

Scientific paper

Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. We consider the corresponding eigenfunctions, and in Theorem 1.1 we prove that the limit inferior of the ergodic sums is bounded for every point 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).

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