Related papers: On the topological essential range and regularity …
In this paper we study topological cocycles for minimal homeomorphisms on a compact metric space. We introduce a notion of an essential range for topological cocycles with values in a locally compact group, and we show that this notion…
We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work we provide a self-contained topological exposition and…
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has been extended and generalized in various…
In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…
After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of…
In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topological spaces. The idea is to replace the standard interval…
We consider continuous extensions of minimal rotations on a locally connected compact group X by arbitrary locally compact Lie groups and prove regularity (i.e. the existence of orbit closures which project onto the whole basis X) in…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of…
We prove that a generic linear cocycle over a minimal base dynamics of finite dimension has the property that the Oseledets splitting with respect to any invariant probability coincides almost everywhere with the finest dominated splitting.…
We wish to investigate some elementary problems concerning topological dynamics revolving around our proposed definition of escaping set. We also discuss the notion of escaping set in the induced dynamics of the hyperspace. Moreover, we…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
In this article, we prove that if a finitely generated group $G$ is not torsion then a necessary and sufficient condition for every full shift over $G$ has (continuous) cocycle superrigidity is that $G$ has one end. It is a topological…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
We consider continuous $SL(2,R)$-cocycles over a minimal homeomorphism of a compact set $K$ of finite dimension. We show that the generic cocycle either is uniformly hyperbolic or has uniform subexponential growth.