* Correspondence: zhjx_19@yahoo. com.cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China Full list of author information is available at the end of the article Abstract Uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity are a natural generalization of both uniformly convexnormed spaces and CAT(0) spaces. In this article, we discuss ...

In this thesis, we establish extreme value (EV) theory and dynamical BorelCantelli lemmas for a class of deterministic chaotic dynamical systems. We establish the distributional convergence (to the three classical extreme value distributions) of the scaled sequence of partial maxima of some time series arising from an observable on systems such as the planar dispersing billiards, Lozi-like maps...

In this note, we obtain verifiable sufficient conditions for the extreme value distribution for a certain class of skew product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of Φ(p) = − log(d(p, ...

Abstract We obtain limit theorems (Stable Laws and Central Limit Theorems, both standard non-standard) thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function is studied in an abstract functional analytic framework, which may be applicable to other classes flows.

Abstract We establish a sufficient condition for continuous map, acting on compact metric space, to have Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, instance, minimal and non-uniquely ergodic map; maps preserving two distinct probability measures with full support; non-trivial homoclinic classes; some non-uniformly expandin...

Suppose (f,X , ν) is a dynamical system and φ : X → R is an observation with a unique maximum at a (generic) point in X . We consider the time series of successive maxima Mn(x) := max{φ(x), . . . ,φ ◦ fn−1(x)}. Recent works have focused on the distributional convergence of such maxima (under suitable normalization) to an extreme value distribution. In this article, for certain dynamical systems...

We introduce a family of area preserving generalized baker’s transformations acting on the unit square and having sharp polynomial rates of mixing for Hölder data. The construction is geometric, relying on the graph of a single variable “cut function”. Each baker’s map B is non-uniformly hyperbolic and while the exact mixing rate depends on B, all polynomial rates can be attained. The analysis ...

We investigate a class of area preserving non-uniformly hyperbolic maps of the two torus. First we establish some results on the regularity of the invariant foliations, then we use this knowledge to estimate the rate of mixing. Stony Brook IMS Preprint #2005/01 January 2005