Finitely-additive measures on the asymptotic foliations of a Markov compactum

Details Finitely-additive measures on the asymptotic foliations of a Markov compactum Finitely-additive measures on the asymptotic foliations of a Markov compactum

2009-02-19

arxiv.org/abs/0902.3303v1

Mathematics

Dynamical Systems

29 pages

Scientific paper

An asymptotic expansion is established for time averages of translation flows on flat surfaces. This result, which extends earlier work of A.Zorich and G.Forni, yields limit theorems for translation flows. The argument, close in spirit to that of G.Forni, uses the approximation of ergodic integrals by holonomy-invariant Hoelder cocycles on trajectories of the flows. The space of holonomy-invariant Hoelder cocycles is finite-dimensional, and is given by an explicit construction. First, a symbolic representation for a uniquely ergodic translation flow is obtained following S.Ito and A.M. Vershik, and then, the space of cocycles is constructed using a family of finitely-additive complex-valued holonomy-invariant measures on the asymptotic foliations of a Markov compactum.

Affiliated with

Also associated with

No associations

Rating

Finitely-additive measures on the asymptotic foliations of a Markov compactum does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finitely-additive measures on the asymptotic foliations of a Markov compactum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finitely-additive measures on the asymptotic foliations of a Markov compactum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-260122