Related papers: On ergodic averages for parabolic product flows

We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of…

We study ergodic theoretical properties of flows on circle bundles over translation surfaces that arise via prequantization, generalizing the theory of Heisenberg nilflows to base surfaces more general than tori; these flows are among the…

We consider the unit speed parametrization of the horocycle flow on infinite Abelian covers of compact surfaces of negative curvature. We prove an asymptotic result for the ergodic integrals of sufficiently regular functions. In the case of…

We provide an abstract framework for the study of certain spectral properties of parabolic systems; specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these…

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…

We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In…

We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic…

We consider ergodic multiflows on a probability space. The general theorem on universal averaging for multiflows is applied to averaging along manifolds in $R^n$.

In equilibrium systems, time and ensemble averages of physical quantities are equivalent due to ergodic exploration of phase space. In driven systems, it is unknown if a similar equivalence of time and ensemble averages exists. We explore…

The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic flow-energy balance model. This model consists of the large scale quasigeostrophic oceanic flow model and the transport…

For any accessible partially hyperbolic homogeneous flow, we show that all smooth time changes are K and hence mixing of all orders. We also establish stable ergodicity for time-one map of these time changes.

We answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials of pairwise differing degrees, converges in $L^{2}$ to the…

Ergodic coverage effectively generates exploratory behaviors for embodied agents by aligning the spatial distribution of the agent's trajectory with a target distribution, where the difference between these two distributions is measured by…

This article is devoted to the study of the historic set of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms…

We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…

Let $\{T^t\}$ be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let $\mu$ be an ergodic measure of maximal entropy. We show that either $\{T^t\}$ is Bernoulli, or…

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly…

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation…