Related papers: Minimality and Gluing Orbit Property
We construct examples of minimal and uniquely ergodic systems realizing all possible behaviors in the interplay of measurable and topological nilfactors. To build such examples, we adapt an idea that stems from Furstenberg's construction of…
In this note we consider dynamical systems $(X,G)$ on a Cantor set $X$ satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems…
We introduce the notions of directional dynamical cubes and directional regionally proximal relation defined via these cubes for a minimal $\mathbb{Z}^d$-system $(X,T_1,\ldots,T_d)$. We study the structural properties of systems that…
We show vanishing results about the infimum of the topological entropy of the geodesic flow of homogeneous smooth four manifolds. We prove that any closed oriented geometric four manifold has zero minimal entropy if and only if it has zero…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using…
It is shown that a relation between entropy and minimal area holds in loop quantum gravity, reminiscent of the Ryu-Takayanagi relation.
This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied.…
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold $M$, and more generally of a finite simplicial complex $X$, vanishes or is positive. These topological conditions are expressed in…
In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then…
The topological entropy dimension is mainly used to distinguish the zero topological entropy systems. Two types of topological entropy dimensions, the classical entropy dimension and the Pesin entropy dimension, are investigated for…
It is known that if each point $x$ of a dynamical system is generic for some invariant measure $\mu_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group…
We consider the notions of topological essential range and regularity for continuous cocycles over minimal $\Z$-systems introduced in \cite{GH} and discuss relations with their generic counterparts. The alternative generic definitions can…
For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…
In this article, we exhibit certain linking properties of periodic orbits of $C^{1+\alpha}$ flows with positive topological entropy on closed 3-manifolds M. It is shown that any such flow contains a link L of periodic orbits and a horseshoe…
We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly…
We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…