2011/06/14 by Xavier Bressaud, Alexander I. Bufetov, Pascal Hubert
Materials Science · Mathematics · #Bounded function #Central limit theorem #Combinatorics #Constant (computer programming) #Eigenfunction #Eigenvalues and eigenvectors #Ergodic theory #Geometric and Algebraic Topology #Invariant measure #Limit (mathematics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #Quasicrystal Structures and Properties #Stationary ergodic process #Statistics #math.CO #math.DS #math.PR #msc:37B10 #msc:37E05
paper · pdf · doi:10.1112/plms/pdu009
published as Proc. London Math. Soc. (2014) · 49 pages, 5 figures
arxiv created 2011/06/14 · openalex publication_date 2014/04/19 · arxiv updated 2014/07/28 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/27
Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1.The functions γ we consider are the corresponding eigenfunctions.In Theorem 1.1 we prove that the limit inferior of the ergodic sums (n, γ(x 0 ) + . . .+ γ(x 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).