Related papers: Finite entropy characterizes topological rigidity

Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…

Let $M$ be a compact Riemannian manifold. The set $\text{F}^{r}(M)$ consisting of sequences $(f_{i})_{i\in\mathbb{Z}}$ of $C^{r}$-diffeomorphisms on $M$ can be endowed with the compact topology or with the strong topology. A notion of…

We study the relationship between the positivity property in a rank 2 cluster algebra, and the property of such an algebra to be tame. More precisely, we show that a rank 2 cluster algebra has a basis of indecomposable positive elements if…

In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding C^2-maps on a compact Riemannian manifold M with uniform bounds on expansion factors and derivatives, we provide…

We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the…

The problem of equivariant rigidity is the $\Gamma$-homeomorphism classification of $\Gamma$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $\Gamma$. In other words, this is the…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…

This is a continuation of the series of notes on the dynamics of quadratic polynomials. We show the following Rigidity Theorem: Any combinatorial class contains at most one quadratic polynomial satisfying the secondary limbs condition with…

An ergodic dynamical system $\mathbf{X}$ is called dominant if it is isomorphic to a generic extension of itself. It was shown in an earlier paper by Glasner, Thouvenot and Weiss that Bernoulli systems with finite entropy are dominant. In…

We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…

We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps $f:X\to Y$ of the class $\alpha$ for wide classes of topological spaces. In particular, we prove that for a topological space $X$…

We consider a class of foliations on the complex projective plane that are determined by a quadratic vector field in a fixed affine neighborhood. Such foliations, as a rule, have an invariant line at infinity. Two foliations with…

Let $G$ be a topological group, let $\phi$ be a continuous endomorphism of $G$ and let $H$ be a closed $\phi$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is,…

We consider closed manifolds that possess a so called rank one ray structure. That is a (flat) affine structure such that the linear part is given by the products of a diagonal transformation and a commuting rotation. We show that closed…

For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…

Let $\mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^\ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system…

We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal…

We develop a theory of additive group actions on affine ind-schemes through a purely algebraic and topological framework. Affine ind-schemes are described via complete, second-countable, linearly topologized rings, and actions of the…

We study topological entropy of exactly Devaney chaotic maps on totally regular continua, i.e. on (topologically) rectifiable curves. After introducing the so-called P-Lipschitz maps (where P is a finite invariant set) we give an upper…