相关论文: Upgrading the Theorem on Local Ergodicity

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table $\Bi := \bigcup_{n\in\N} [n,n+1] \times…

We present a quantum ergodicity theorem for fixed spectral window and sequences of compact hyperbolic surfaces converging to the hyperbolic plane in the sense of Benjamini and Schramm. This addresses a question posed by Colin de…

Given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is conjectured by several authors that for sufficiently hyperbolic dynamical systems,…

A hyperbolic set on a compact manifold M, satisfies the property: given two of your any points p and q, such that for all positive \epsilon>0, there is a trajectory in the hyperbolic set from a point \epsilon-close to p to a point…

We introduce the notion of common conditional expectation to investigate Birkhoff's ergodic theorem and subadditive ergodic theorem for invariant upper probabilities. If in addition, the upper probability is ergodic, we construct an…

We study higher order expansions both in the Berry-Ess\'een estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical…

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

We consider dynamics of scalar semilinear parabolic equations on bounded intervals with periodic boundary conditions, and on the entire real line, with a general nonlinearity $g(t,x,u,u_x)$ either not depending on $t$, or periodic in $t$.…

We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result…

Recently, Chen et al introduced an alternative form of Hardy's paradox for $2$-settings and high-dimensional systems [Phy. Rev. A 88, 062116 (2013)], in which there is a great progress in improving the maximum probability of the nonlocal…

We consider dissipative relativistic fluid theories on a fixed flat, compact, globally hyperbolic, Lorentzian manifold. We prove that for all initial data in a small enough neighborhood of the equilibrium states (in an appropriate Sobolev…

We give elementary constructions of factors of nonsingular Bernoulli shifts. In particular, we show that all nonsingular Bernoulli shifts on a finite number of symbols which satisfy the Doeblin condition have a factor that is equivalent to…

In this work we exhibit a new criteria for ergodicity of diffeomorphisms involving conditions on Lyapunov exponents and general position of some invariant manifolds. On one hand we derive uniqueness of SRB-measures for transitive surface…

In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize…

We prove that the projective complex algebraic varieties admitting a large complex local system satisfy a strong version of the Green-Griffiths-Lang conjecture.

Statistical equilibration of energies in a slow-fast system is a fundamental open problem in physics. In a recent paper, it was shown that the equilibration rate in a springy billiard can remain strictly positive in the limit of vanishing…

We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C^\infty$ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric…

We investigate the relationship between the Lyapunov exponents of periodic trajectories, the average and fluctuations of Lyapunov exponents of ergodic trajectories, and the ergodic autocorrelation time for the two-dimensional hyperbola…

In the case of smooth non-invertible maps which are hyperbolic on folded basic sets $\Lambda$, we give approximations for the Gibbs states (equilibrium measures) of arbitrary H\"{o}lder potentials, with the help of weighted sums of atomic…