We prove that the continuous correlation function decrease polynomially for two families of billiard studied by Chernov and Zhang. The main computation is to show that the return function is Holder on stable and unstable manifold.
We estimate from below the topological entropy of the generalized Bunimovich stadium billiards. We do it for long billiard tables, and find the limit of estimates as the length goes to infinity.
We construct an Arnoux-Rauzy word for which the set of all differences of two abelianized factors is equal to $\mathbb{Z}^3$. In particular, the imbalance of this word is infinite - and its Rauzy fractal is unbounded in all directions of the plane.
For classical Bernoulli convolutions, the Rajchman property, i.e. the convergence to zero at infinity of the Fourier transform, was characterized by successive works of Erd{ö}s [2] and Salem [12]. We prove weak forms of their results for general self-similar measures associated to affine contractions of the real line.
We describe characteristic factors for certain averages arising from commuting actions of locally compact, second-countable, amenable groups. Under some ergodicity assumptions we use these factors to prove a form of multiple recurrence for three such actions.
We discuss automorphisms and pseudo-automorphisms on blowups of complex projective space with an eye to finding ones with interesting dynamical behavior.
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.
This is a review article on the distributions of entry and return times in dynamical systems which discusses recent results for systems of positive entropy.
We extend the concept of Lyapunov 1-forms for the case of diffu- sion processes to study its asymptotic behavior. We give some examples and a condition for the existence of these objects.
We prove that, for a Ruelle-expanding map, the zeta function is rational and the topological entropy is equal to the exponential growth rate of the periodic points.
Given any Liouville number $α$, it is shown that various subspaces are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms of the circle with rotation number $α$.
In this article, we improve previous results on exponential stability for analytic and Gevrey perturbations of quasi-convex integrable Hamiltonian systems. In particular, this provides a sharper upper bound on the speed of Arnold diffusion which we believe to be optimal.
In the family of degree $d$ polynomials the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier $e^{iθ}$ are shown to equiditribute the bifurcation current.