Related papers: Multifractal analysis of some multiple ergodic ave…
In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, it is applied to the analytic quasi-periodic Jacobi cocycles. We show that if the Lyapunov exponent of…
Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the literature for decades. In this paper, we review and extend the…
We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\neq j$. The limiting behavior of such…
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a…
It follows from Oseledec Multiplicative Ergodic Theorem (or Kingman's Sub-additional Ergodic Theorem) that the set of `non-typical' points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect…
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 study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…
We introduce a new class of sparse sequences that are ergodic and pointwise universally $L^2$-good for ergodic averages. That is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions.…
By definition, a map quasiperiodic on a set $X$ if the map is conjugate to a pure rotation. Suppose we have a trajectory $(x_n)$ that we suspect is quasiperiodic. How do we determine if it is? In this paper we show how to compute the…
Let $f$ be a holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$ of algebraic degree at least $2$ and let $X \subseteq \mathbb{C}\mathbb{P}^k$ be an uniformly expanding set. In this paper, we study multifractal analysis of equilibrium…
We find limits of some multiple ergodic averages, generalizing a result of Bergelson to the setting of two commuting transformations and actions of amenable groups.
In this paper, we establish a noncommutative maximal inequality for ergodic averages with respect to the set $\{k^t|k=1,2,3,...\}$ acting on noncommutative $L_p$ spaces for $p>\frac{\sqrt{5}+1}{2}$.
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
We prove the equivariant divergence formula for the axiom A flow attractors, which is a recursive formula for perturbation of transfer operators of physical measures along center-unstable manifolds. Hence the linear response acquires an…
We use techniques of proof mining to obtain a computable and uniform rate of metastability (in the sense of Tao) for the mean ergodic theorem for a finite number of commuting linear contractive operators on a uniformly convex Banach space.
In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation.…
We consider weighted ergodic averages indexed by primes, where the weight depends on the prime, and is a "trace function" coming from algebraic geometry. We obtain extensions the classical mean-ergodic and pointwise ergodic theorems, as…
In the first part of the paper the natural scheme for proving noncommutative individual ergodic theorems for multiple sequences is described and applied to obtain results on unrestricted convergence of multiaverages. In the second part…
We perform a multifractal analysis of the growth rate of the number of cusp windings for the geodesic flow on hyperbolic surfaces with $m \geq 1$ cusps. Our main theorem establishes a conditional variational principle for the Hausdorff…