Related papers: On the asymptotic behavior of cocycles over flows

We consider smooth area-preserving flows (also known as locally Hamiltonian flows) on surfaces of genus $g\geq 1$ and study ergodic integrals of smooth observables along the flow trajectories. We show that these integrals display a…

The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a…

We prove that the Birkhoff pointwise ergodic theorem and the Oseledets multiplicative ergodic theorem hold for every flat surface in almost every direction. The proofs rely on the strong law of large numbers, and on recent rigidity results…

In 1949 V.A. Rokhlin introduced into ergodic theory the k-fold mixing and puzzled the mathematical community with the problem of the mismatch of these invariants. Here's what Rokhlin wrote: "The proposed work arose from the author's…

Ten years ago A. Zorich discovered, by computer experiments on interval exchange transformations, some striking new power laws for the ergodic integrals of generic non-exact Hamiltonian flows on higher genus surfaces. In Zorich's later work…

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…

Given $1\leq p<\infty$, we show that ergodic flows in the $L^p$-space over a $\sigma$-finite measure space generated by strongly continuous semigroups of Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic…

The celebrated Birkhoff Ergodic Theorem asserts that, for an ergodic map, orbits of almost every point equidistributes when sampled at integer times. This result was generalized by Bourgain to many natural sparse subsets of the integers. On…

The classical Multiplicative Ergodic Theorem (MET) of Oseledets is generalized here to cocycles taking values in a semi-finite von Neumann algebra. This allows for a continuous Lyapunov distribution.

In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in…

The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on…

We apply a method inspired by Ratner's work on quantitative mixing for the geodesic flow (Ergod. Theory Dyn. Syst., 1987) and developed by Burger (Duke Math. J., 1990) to study ergodic integrals for horocycle flows. We derive an explicit…

Oseledets' celebrated Multiplicative Ergodic Theorem (MET) is concerned with the exponential growth rates of vectors under the action of a linear cocycle on R^d. When the linear actions are invertible, the MET guarantees an…

Birkhoff's theorem states that for an ergodic automorphism, the time averages converge to the space average. Given sequence $\psi(n)\to+0$, U. Krengel proved that for any ergodic automorphism there is an indicator such that the…

We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…

We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…

We show that ergodic flows in noncommutative fully symmetric spaces (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford-Schwartz operators and modulated by bounded Besicovitch almost…

The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…

The ergodic hypothesis outgrew from the ancient conception of motion as periodic or quasi periodic. It did cause a revision of our views of motion, particularly through Boltzmann and Poincar\'e: we discuss how Boltmann's conception of…

We prove almost sure ergodic theorems for a class of systems called quasistatic dynamical systems. These results are needed, because the usual theorem due to Birkhoff does not apply in the absence of invariant measures. We also introduce…