Strongly Ergodic Sequences of Integers and the Individual Ergodic Theorem

Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Powers of sequences and convergence of ergodic averages

A sequence (sn) of integers is good for the mean ergodic theorem if for each invertible measure preserving system (X, B, µ, T) and any bounded measurable function f , the averages 1 N P N n=1 f (T sn x) converge in the L 2 (µ) norm. We construct a sequence (sn) that is good for the mean ergodic theorem, but the sequence (s 2 n) is not. Furthermore, we show that for any set of bad exponents B, t...

Ergodic Averages for Independent Polynomials and Applications

Szemerédi’s Theorem states that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman generalized this, showing that sets of integers with positive upper density contain arbitrarily long polynomial configurations; Szemerédi’s Theorem corresponds to the linear case of the polynomial theorem. We focus on the case farthest from the l...