Related papers: On the irregular points for systems with the shado…

We consider a diffeomorphism f of a compact manifold M which is Almost Axiom A, i.e. f is hyperbolic in a neighborhood of some compact f-invariant set, except in some singular set of neutral points. We prove that if there exists some…

In this study, utilizing a specific exponential weighting function, we investigate the uniform exponential convergence of weighted Birkhoff averages along decaying waves and delve into several related variants. A key distinction from…

Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of…

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.

We prove that an asymptotically linear Hamiltonian diffeomorphism of the standard symplectic vector space, which is non-degenerate and unitary at infinity and approaches its linear map at infinity quickly enough, has infinitely many…

The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a…

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…

We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…

We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the…

We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for $C^\infty$ surface diffeomorphisms [9]. As a consequence we show that any $C^r$, $r > 1$, smooth surface diffeomorphism $f$ with…

We construct mesures supported on a compact subset E of the real line having zero principal value of their Cauchy integral a.e. on E with respect to Lebesgue measure and having singular components. E is sufficiently regular (Widom property…

The ubiquity of optical coherence arising from its importance in everything from astronomy to photovoltaics means that underlying assumptions such as stationarity and ergodicity can become implicit. When these assumptions become implicit,…

Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global schemes. Existing sufficient criteria for…

For any C1 diffeomorphism with dominated splitting we consider a nonempty set of invariant measures which describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the…

In this paper, we study the structure of Birkhoff spectra for hyperbolic dynamical systems. Given a H\"older observable \(f\) on a basic set \(\Lambda\), we obtain the following results: First, we characterize when the Birkhoff spectrum of…

We show that the continuity property of Lyapunov exponents proved in \cite{BCS-Exponents} for smooth surface diffeomorphisms extends to smooth interval maps, in the case when the map only has non-flat critical points and the entropies…

This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The…

We consider smooth locally Hamiltonian flows on compact surfaces of genus $g\geq 2$ to prove their deviation of Birkhoff integrals for smooth observables. Our work generalizes results of Forni and Bufetov which prove the existence of…

We prove that if two topologically free and entropy regular actions of countable sofic groups on compact metrizable spaces are continuously orbit equivalent, and each group either (i) contains a w-normal amenable subgroup which is neither…

In this work, we introduce the notion of entropy at infinity, and define a wide class of noncompact manifolds with negative curvature, those which admit a critical gap between entropy at infinity and topological entropy. We call them…