arXiv subjects

Pramod Das

Publications and source records attributed to Pramod Das.

4 recordsLinked to original sources

arXiv2018

GH-stability and Spectral Decomposition for Group Actions

We study expansivity and the shadowing property for finitely generated group actions on metric spaces. We consider the projecting and lifting problems for actions having these properties. We prove that every expansive action with the shadowing property is strongly $GH$-stable (Gromov-Hausdorff stable). Finally, we introduce sequential shadowing property for finitely generated group actions on metric spaces and show that such shadowing is strong enough to imply the spectral decomposition property.

math.DS↗

arXiv2018

Measure Expansivity and Specification for Pointwise Dynamics

We introduce pointwise measure expansivity for bi-measurable maps. We show through examples that this notion is weaker than measure expansivity. In spite of this fact, we show that many results for measure expansive systems hold true for pointwise systems as well. Then, we study the concept of mixing, specification and chaos at a point in the phase space of a continuous map. We show that mixing at a shadowable point is not sufficient for it to be a specification point, but mixing of the map force a shadowable point to be a specification point. We prove that periodic specification points are Devaney chaotic point. Finally, we show that existence of two distinct specification points is sufficient for a map to have positive Bowen entropy.

math.DS↗

arXiv2018

Various Non-autonomous Notions for Borel Measures

We introduce and investigate the notions of expansiveness, topological stability and persistence for Borel measures with respect to time varying bi-measurable maps on metric spaces. We prove that expansive persistent measures are topologically stable in the class of all time varying homeomorphisms.

math.DS↗

arXiv2018

Stability Theorems for Group Actions on Uniform Spaces

We extend the notions of topological stability, shadowing and persistence from homeomorphisms to finitely generated group actions on uniform spaces and prove that an expansive action with either shadowing or persistence is topologically stable. Using the concept of null set of a Borel measure $μ$, we introduce the notions of $μ$-expansivity, $μ$-topological stability, $μ$-shadowing and $μ$-persistence for finitely generated group actions on uniform spaces and show that a $μ$-expansive action with either $μ$-shadowing or $μ$-persistence is $μ$-topologically stable.

math.DS↗