Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1. Issue 2 (19th April 2014)

• Record Type: Journal Article
• Authors: Bressaud, Xavier; Bufetov, Alexander I.; Hubert, Pascal
• Is Part Of: Proceedings of the London Mathematical Society. Volume 109:Issue 2(2014:Aug.)
• Page Start: 483
• Page End: 522
• Publication Date: 2014-04-19
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdu009
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract : Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. The functionsγ 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 pointx 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).