Publication Date:
2014-08-19
Description:
Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. The functions $\gamma$ we consider are the corresponding eigenfunctions. In Theorem 1.1, we prove that the limit inferior of the ergodic sums $(n, \gamma (x_0) + \cdots + \gamma (x_{n-1}))_{n\in {\mathbb N} }$ 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 (Theorems 1.3 and 1.10).
Print ISSN:
0024-6115
Electronic ISSN:
1460-244X
Topics:
Mathematics
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