Related papers: Weak disks of Denjoy minimal sets

We call a dynamical system on a measurable metric space {\em measure-expansive} if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces…

We study a class of homeomorphisms of surfaces collectively known as linked-twist maps. We introduce an abstract definition which enables us to give a precise characterisation of a property observed by other authors, namely that such maps…

This study examines the tree models of mildly dissipative diffeomorphisms on the disk $\D$. These models are one-dimensional dynamical systems with ergodic aperiodic data as well as some properties of the original dynamics. The focus of…

We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…

Let $f: M \to M$ be a $C^{1+\alpha}$ map/diffeomorphism of a compact Riemannian manifold $M$ and $\mu$ be an expanding/hyperbolic ergodic $f$-invariant Borel probability measure on $M$. Assume $f$ is average conformal expanding/hyperbolic…

We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…

We discuss the dynamics of smooth diffeomorphisms of the disc with vanishing topological entropy which satisfy the mild dissipation property introduced in [CP]. In particular it contains the H\'enon maps with Jacobian up to 1/4. We prove…

In this paper we investigate maps of the two-torus $\mathbb{T}^2$ of the form $T(x,y)=(x+\omega,g(x)+f(y))$ for Diophantine $\omega\in\mathbb{T}$ and for a class of maps $f,g:\mathbb{T}\to\mathbb{T}$, where each $g$ is strictly monotone and…

The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…

We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the $d$-bar metric. As a consequence the set of ergodic measures of such a…

Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…

We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…

We construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [Israel J. Math. 192 (2012), no. 2, 785--817]. Elaborating on our examples we…

We extend anti-classification results in ergodic theory to the collection of weakly mixing systems by proving that the isomorphism relation as well as the Kakutani equivalence relation of weakly mixing invertible measure-preserving…

We prove that under some assumptions on how points escape to infinity in the universal cover, homeomorphisms of hyperbolic 3-manifolds are forced to have several invariant sets (in particular, they cannot be minimal). For this, we use some…

We prove that topologically generic orbits of C0 transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the minimum weak* compact set of invariant probabilities, that…

For a surface diffeomorphism, a compact invariant locally maximal set $W$ and some subset $A\subset W$ we study the $A$-exceptional set, that is, the set of points whose orbits do not accumulate at $A$. We show that if the Hausdorff…

We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…

The main aim of the paper is to introduce a new class of (semigroup-valued) measures that are ultrahomogeneous on the Boolean algebra of all clopen subsets of the Cantor space and to study their automorphism groups. A characterisation, in…

We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…