Chaos for induced hyperspace maps

DOI10.1016/j.chaos.2004.11.089zbMath1071.37012OpenAlexW2135843380MaRDI QIDQ2483604

John Banks

Publication date: 25 July 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://polipapers.upv.es/index.php/AGT/article/view/1724

zbMATH Keywords

topological transitivitysensitive dependence on initial conditionshyperspacesinduced mapsweak topological mixingperiodic pints

Mathematics Subject Classification ID

Related Items (74)

Weak stability of non-autonomous discrete dynamical systems ⋮ Monotone maps on dendrites and their induced maps ⋮ Topological properties on hyperspace of group actions ⋮ Some notes on induced functions and group actions on hyperspaces ⋮ Dynamics of multivalued linear operators ⋮ Unnamed Item ⋮ A note on periodic points of dendrite maps and their induced maps ⋮ Almost minimal systems and periodicity in hyperspaces ⋮ Lifting Dynamical Properties to Hyperspaces ⋮ On turbulent, erratic and other dynamical properties of Zadeh's extensions ⋮ Mixing properties of set-valued maps on hyperspaces via Furstenberg families ⋮ Difference between Devaney chaos associated with two systems ⋮ The set-valued mapping induced by a non-minimal transitive system is Li-Yorke chaotic ⋮ A framework of induced hyperspace dynamical systems equipped with the hit-or-miss topology ⋮ Characterizing ergodicity of induced hyperspace dynamical systems ⋮ Set-valued chaos in linear dynamics ⋮ Sensitivity for topologically double ergodic dynamical systems ⋮ On the transitivity of multifunctions and density of orbits in generalized topological spaces ⋮ Furstenberg families, sensitivity and the space of probability measures ⋮ Topological entropy of the extended tree map on the space of fuzzy numbers ⋮ Martelli's chaos in inverse limit dynamical systems and hyperspace dynamical systems ⋮ Some chaotic properties of discrete fuzzy dynamical systems ⋮ Topological Dynamics of Zadeh’s Extension on Upper Semi-Continuous Fuzzy Sets ⋮ On recurrence and entropy in the hyperspace of continua in dimension one ⋮ Polynomial entropy of induced maps of circle and interval homeomorphisms ⋮ Shadowing property of hyperspace for free semigroup actions ⋮ Periodic points and transitivity on dendrites ⋮ Dynamics of induced systems ⋮ When are all closed subsets recurrent? ⋮ Dynamic to Quotients of Hyperspaces ⋮ Relative uniformly positive entropy of induced amenable group actions ⋮ Topological entropy of induced circle maps on hyperspaces ⋮ On Devaney chaotic induced fuzzy and set-valued dynamical systems ⋮ Dynamic properties for the induced maps on n-fold symmetric product suspensions ⋮ A note on stronger forms of sensitivity for dynamical systems ⋮ When is a dynamical system mean sensitive? ⋮ Equicontinuity of maps on dendrites ⋮ Recurrence properties and disjointness on the induced spaces ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Chaos in non-autonomous discrete systems and their induced set-valued systems ⋮ Characterizing mixing, weak mixing and transitivity of induced hyperspace dynamical systems ⋮ Hyperconvergence in topological dynamics ⋮ Sensitivity and strong sensitivity on induced dynamical systems ⋮ Chain transitivity in hyperspaces ⋮ On the dynamics of subcontinua of a tree ⋮ Devaney's chaos for maps on \(G\)-spaces ⋮ Some chaotic properties of Zadeh's extensions ⋮ FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS ⋮ Dynamical systems over the space of upper semicontinuous fuzzy sets ⋮ On metrization of the hit-or-miss topology using Alexandroff compactification ⋮ On fuzzy entropy and topological entropy of fuzzy extensions of dynamical systems ⋮ Topological entropy for induced hyperspace maps ⋮ Topological entropy for set valued maps ⋮ Inducing sensitivity on hyperspaces ⋮ On fuzzifications of non-autonomous dynamical systems ⋮ Dynamics of Weakly Mixing Nonautonomous Systems ⋮ Inducing Sensitivity of Fuzzified Dynamical Systems ⋮ Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems ⋮ On local aspects of sensitivity in topological dynamics ⋮ Sensitivity and transitivity of fuzzified dynamical systems ⋮ Topological entropy and chaos for maps induced on hyperspaces ⋮ Sensitivity for set-valued maps induced by \(M\)-systems ⋮ The transitivity of induced maps ⋮ Chaos on hyperspaces ⋮ Induced dynamics on the hyperspaces ⋮ On local aspects of topological transitivity and weak mixing in set-valued discrete systems ⋮ Shadowing for induced maps of hyperspaces ⋮ On the transitivity and sensitivity of group actions ⋮ On the topological entropy of induced transformations for free semigroup action ⋮ Dynamics of Nonautonomous Discrete Dynamical Systems ⋮ Sensitivity of set-valued discrete systems ⋮ Entropy of induced maps of regular curves homeomorphisms ⋮ \(\mathcal{F}\)-sensitivity and multi-sensitivity of hyperspatial dynamical systems ⋮ Recent development of chaos theory in topological dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractals and hyperspaces
• On maps with dense orbits and the definition of chaos
• A note on transitivity in set-valued discrete systems.
• Topological mapping properties defined by digraphs
• Dynamical systems, measures, and fractals via domain theory
• On Devaney's Definition of Chaos
• Regular periodic decompositions for topologically transitive maps
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Topologies on Spaces of Subsets

This page was built for publication: Chaos for induced hyperspace maps