Related papers: $\omega$-recurrence in cocycles

We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…

We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) \times \mathbb{R}}\to{[0, 1) \times \mathbb{R}},\quad {T_f(x, t)}:={(T(x),…

We study strange non-chaotic attractors in a class of quasiperiodically forced monotone interval maps known as pinched skew products. We prove that the probability of positive time-N Lyapunov exponents, with respect to the unique physical…

This is the first article in a series that aims at classifying partial sections of flows, that is a general family of transverse surfaces. In this part, we deal with the dynamical aspect of the question. Given a flow on a compact manifold…

In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…

In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise,…

A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the…

We prove that vertex-reinforced random walk on the integers with weight of order k to the power alpha, for alpha in [0, 1/2), is recurrent. This confirms a conjecture of Volkov for alpha<1/2. The conjecture for alpha in [1/2, 1) remains…

We exhibit an example of discontinuity point for the Lyapunov exponents as a function of the cocycle in the $\alpha$-H\"older topology. The linear cocycle taking values in $SL(2, \mathbb{R})$ is locally constant and defined over a Bernoulli…

We study the problem of estimating the maximal Lyapunov exponent of dominated cocycles. In particular we are concerned with cocycles over Gibbs states on shifts of finite type for which both the function defining the cocycle and the…

Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent…

In the present paper we prove that densely, with respect to an $L^p$-like topology, the Lyapunov exponents associated to linear continuous-time cocycles $\Phi:\mathbb{R}\times M\to \text{GL}(2,\mathbb{R})$ induced by second order linear…

For linear random dynamical systems in a separable Banach space $X$, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-$k$, which present a (quasi)-equivalence relation between the…

Let X be a projective scheme over a finite field. In this paper, we consider the asymptotic behavior of the number of effective cycles on X with bounded degree as it goes to the infinity. By this estimate, we can define a certain kind of…

We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface…

The ergodic properties of two uncoupled oscillators, a horizontal and vertical one, residing in a class of non rectangular star-shaped polygons with only vertical and horizontal boundaries and impacting elastically from its boundaries are…

We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…

A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.

We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…

In this paper we study ergodic optimization problems for typical cocycles. We consider one-step $SL(2,\mathbb{R})$-cocycles that satisfy pinching and twisting conditions. We prove that the Lyapunov maximizing measures have zero entropy…