Related papers: Mean Topological Dimension for random bundle trans…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
We study the metric mean dimension of $\Phi$-irregular set $I_{\Phi}(f)$ in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class $Y$, the values…
Let $\pi:(X,G)\to (Y,G) $ be a factor map between continuous actions of a sofic group $G$, we study sofic conditional mean dimension and relative sofic mean dimension introduced in \cite{LBB2} and \cite{LB}, respectively. We obtain that if…
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…
The quantization problem for random fractals presents unique challenges due to the lack of uniform geometric scaling inherent in deterministic systems. In this article, we establish the almost sure quantization dimension for a class of…
This paper is a continuation of our work on D. Voiculescu's topological free entropy dimension in unital C*-algebras. In this paper we first prove the topological free entropy dimension of a MF-nuclear and inner QD algebra is irrelevant to…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded.
The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For…
We study the directional entropy of the dynamical system associated to a $\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some…
We prove that the Hausdorff dimension of an average conformal repeller is stable under random perturbations. Our perturbation model uses the notion of a bundle random dynamical system.
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in…
We show that if a closed manifold M admits an F-structure (possibly of rank 0) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial circle action. As a corollary we obtain that the simplicial volume…
The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas…
In the present work we consider the behavior of the geodesic flow on the unit tangent bundle of the 2-torus $T^2$ for an arbitrary Riemannian metric. A natural non-negative quantity which measures the complexity of the geodesic flow is the…
We prove that the homeomorphisms of a compact manifold with dimension one have zero topological emergence, whereas in dimension greater than one the topological emergence of a C^0-generic conservative homeomorphism is maximal, equal to the…
We provide an estimate of the amenable category of oriented closed connected complete affine manifolds whose fundamental group contains an infinite amenable normal subgroup. As an application we show that all such manifolds have zero…
The Hurewicz theorem is a fundamental result in classical dimension theory concerning continuous maps which lower topological dimension. We study whether or not its analogue holds for mean dimension of dynamical systems. Our first main…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…