Abstract. We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banach-spacevalued additive functions. We then give a necessary and sufficient condition on a minimal subshift to allow for a uniform subadditive ergodic theorem. This provides in par...

We show the following. Theorem. Let M be an finite-state ergodic time-reversible Markov chain with transition matrix P and conductanceφ. Let λ ∈ (0, 1) be an eigenvalue of P. Then, φ + λ 6 1 This strengthens the well-known [4, 3, 2, 1, 5] inequality λ 6 1− φ2/2. We obtain our result by a slight variation in the proof method in [5, 4]; the same method was used earlier in [6] to obtain the same i...

Let X=G/Γ, where G is a Lie group and Γ lattice in G, let U be an open subset of X, {gt} one-parameter subgroup G. Consider the set points X whose gt-orbit misses U; it has measure zero if flow ergodic. It been conjectured that this Hausdorff dimension strictly smaller than X. This conjecture proved when compact or simple real rank 1. In paper we prove for case G=SLm+n(R), Γ=SLm+n(Z) gt=diag(en...

Suppose G is a connected, simple, real Lie group with R-rank (G) 2, M is an ergodic G-space with invariant probability measure p, and a: G x M ~ s Homeo(T) is a Bore1 cocycle.We use an argument of E. Ghys to show that there is a G-invariant probability measure v on the skew product M xy, T, such that the projection of v to M is p. Furthermore, if a(G x M ) c ~ i f f ( T ) , then v can be taken ...

Let Σ be a compact orientable surface with genus g and n boundary components B = (B1, . . . , Bn). Let c = (c1, . . . , cn) ∈ [−2, 2]n. Then the mapping class group MCG of Σ acts on the relative SU(2)-character variety XC := HomC(π,SU(2))/SU(2), comprising conjugacy classes of representations ρ with tr(ρ(Bi)) = ci. This action preserves a symplectic structure on the smooth part of XC , and the ...

Ergodic systems, being indecomposable are important part of the study dynamical systems but if a system is not ergodic, it natural to ask following question: Is possible split into ergodic in such way that former reduces latter ones? Also, will be interesting see ones inherit some properties one. This document answers this question for measurable maps defined on complete separable metric spaces...

The Bratteli diagram is an infinite graph which reflects the structure of projections in a C∗-algebra. We prove that every strictly ergodic unimodular Bratteli diagram of rank 2g + m − 1 gives rise to a minimal geodesic lamination with the m-component principal region on a surface of genus g ≥ 1. The proof is based on the Morse theory of the recurrent geodesics on the hyperbolic surfaces.