An Alternative Definition of Topological Entropy for Amenable Group Actions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-021-09547-0
Abstract: We extend the definition of topological entropy for any (not necessarily continuous) amenable groups acting on a compact space by defining entropy of arbitrary subsets of a product space. We investigate how this new notion… read more here.
Keywords: topological entropy; definition topological; entropy; entropy amenable ... See more keywords
Estimation of topological entropy in random dynamical systems
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.12.030
Abstract: Abstract For C r ( r > 1 ) random dynamical systems F on a compact smooth Riemannian manifold M, the fiber topological entropy is bounded above by an integral formula. Particularly, for the C… read more here.
Keywords: random dynamical; entropy random; topological entropy; dynamical systems ... See more keywords
Topological entropy dimension for nonautonomous dynamical systems
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.03.065
Abstract: Abstract In this paper, the topological entropy dimension for nonautonomous dynamical systems is studied. This entropy dimension measures the complexity of the systems with zero entropy via the subexponential growth rate of orbits. Some basic… read more here.
Keywords: topological entropy; entropy dimension; dimension nonautonomous; dynamical systems ... See more keywords
Topological entropy for locally linearly compact vector spaces
Sign Up to like & getrecommendations! Published in 2019 at "Topology and its Applications"
DOI: 10.1016/j.topol.2018.11.009
Abstract: Abstract By analogy with the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study the… read more here.
Keywords: topological entropy; linearly compact; compact vector; entropy ... See more keywords
Entropy continuity for interval maps with holes
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DOI: 10.1017/etds.2016.115
Abstract: We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole at a uniform rate.… read more here.
Keywords: topological entropy; continuity interval; interval maps; maps holes ... See more keywords
Topological chaos in active nematics
Sign Up to like & getrecommendations! Published in 2019 at "Nature Physics"
DOI: 10.1038/s41567-019-0600-y
Abstract: Active nematics are out-of-equilibrium fluids composed of rod-like subunits, which can generate large-scale, self-driven flows. We examine a microtubule-kinesin-based active nematic confined to two dimensions, exhibiting chaotic flows with moving topological defects. Applying tools from… read more here.
Keywords: chaos active; topological chaos; topological entropy; active nematics ... See more keywords
Topological entropy of continuous self-maps on closed surfaces
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2019.1710141
Abstract: The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of… read more here.
Keywords: self maps; entropy continuous; topological entropy; maps closed ... See more keywords
Quasi-graphs, zero entropy and measures with discrete spectrum
Sign Up to like & getrecommendations! Published in 2022 at "Nonlinearity"
DOI: 10.1088/1361-6544/ac4b3a
Abstract: In this paper, we study dynamics of maps on quasi-graphs and characterise their invariant measures. In particular, we prove that every invariant measure of a quasi-graph map with zero topological entropy has discrete spectrum. Additionally,… read more here.
Keywords: discrete spectrum; entropy; quasi graphs; topological entropy ... See more keywords
Worst-case topological entropy and minimal data rate for state estimation of switched linear systems
Sign Up to like & getrecommendations! Published in 2022 at "Communications of the ACM"
DOI: 10.1145/3505269
Abstract: In this paper, we study the problem of estimating the state of a switched linear system (SLS), when the observation of the system is subject to communication constraints. We introduce the concept of worst-case topological… read more here.
Keywords: state; case topological; switched linear; worst case ... See more keywords
Topological Entropy of Free Semigroup Actions Generated by Proper Maps for Noncompact Subsets
Sign Up to like & getrecommendations! Published in 2021 at "Taiwanese Journal of Mathematics"
DOI: 10.11650/tjm/210903
Abstract: In this paper, we introduce three notions of topological entropy of a free semigroup action generated by proper maps for noncompact subsets, which extends the notions defined by Ju et al. [13] and Ma et… read more here.
Keywords: free semigroup; proper maps; topological entropy; generated proper ... See more keywords