Topological entropy and chaos for maps induced on hyperspaces
From MaRDI portal
Publication:2519651
DOI10.1016/j.chaos.2005.12.033zbMath1152.37306OpenAlexW2071624597MaRDI QIDQ2519651
Piotr Oprocha, Dominik Kwietniak
Publication date: 27 January 2009
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.chaos.2005.12.033
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Topological entropy (37B40)
Related Items
Chaos for multivalued maps and induced hyperspace maps ⋮ Weak stability of non-autonomous discrete dynamical systems ⋮ Monotone maps on dendrites and their induced maps ⋮ Unnamed Item ⋮ Almost minimal systems and periodicity in hyperspaces ⋮ On Some Sets of Almost Continuous Functions which Locally Aproximate a Fixed Function ⋮ 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 ⋮ Unnamed Item ⋮ Topological structure and entropy of mixing graph maps ⋮ Chaotic points of multifunctions ⋮ The set-valued mapping induced by a non-minimal transitive system is Li-Yorke chaotic ⋮ On two notions of topological entropy for noncompact spaces ⋮ 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 ⋮ Topological entropy of the extended tree map on the space of fuzzy numbers ⋮ The generalized entropy in the generalized topological spaces ⋮ Chaos of Transformations Induced Onto the Space of Probability Measures ⋮ 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 ⋮ Chaos to Multiple Mappings ⋮ Dynamics and topological entropy for Zadeh's extension of a compact system ⋮ Parametric topological entropy of families of multivalued maps in topological spaces and induced hyperspace maps ⋮ Shadowing, topological entropy and recurrence of induced Morse-Smale diffeomorphism ⋮ Topological entropy of induced circle maps on hyperspaces ⋮ On some dense sets in the space of dynamical systems ⋮ A note on stronger forms of sensitivity for dynamical systems ⋮ When is a dynamical system mean sensitive? ⋮ Fuzzy topological entropy of fuzzy continuous functions on fuzzy topological spaces ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Chain transitive induced interval maps on continua ⋮ Chaos in non-autonomous discrete systems and their induced set-valued systems ⋮ Shadowing, entropy and a homeomorphism of the pseudoarc ⋮ Hereditarily indecomposable inverse limits of graphs: shadowing, mixing and exactness ⋮ Characterizing mixing, weak mixing and transitivity of induced hyperspace dynamical systems ⋮ Nielsen number, impulsive differential equations and problem of Jean Leray ⋮ Chain transitivity in hyperspaces ⋮ On the dynamics of subcontinua of a tree ⋮ Minimal spaces with cyclic group of homeomorphisms ⋮ FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS ⋮ Topological entropy of fuzzified dynamical systems ⋮ Topological entropy of continuous functions on topological spaces ⋮ Topological entropy for set valued maps ⋮ Inducing sensitivity on hyperspaces ⋮ The fixed-point property under induced interval maps of continua ⋮ Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems ⋮ Sensitivity for set-valued maps induced by \(M\)-systems ⋮ The transitivity of induced maps ⋮ Uniformly positive entropy of induced transformations ⋮ Chaos on hyperspaces ⋮ Induced dynamics on the hyperspaces ⋮ Shadowing for induced maps of hyperspaces ⋮ Dynamics of Nonautonomous Discrete Dynamical Systems ⋮ CHAOS ON HYPERSPACE ⋮ Sensitivity of set-valued discrete systems ⋮ Entropy of induced maps of regular curves homeomorphisms ⋮ \(\mathcal{F}\)-sensitivity and multi-sensitivity of hyperspatial dynamical systems ⋮ Topological entropy of multivalued maps in topological spaces and hyperspaces
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Devaney's chaotic on induced maps of hyperspace
- Exact Devaney chaos and entropy
- Topological dynamics of transformations induced on the space of probability measures
- Ergodic theory on compact spaces
- A splitting theorem for transitive maps
- A note on transitivity in set-valued discrete systems.
- On chaotic set-valued discrete dynamical systems
- Dynamical systems, measures, and fractals via domain theory
- Chaos for induced hyperspace maps
- Robinson's chaos in set-valued discrete systems
- Set-valued discrete chaos
- On mixing property in set-valued discrete systems
- Topological entropy for induced hyperspace maps
- Regular periodic decompositions for topologically transitive maps
- Quasi-Factors of Zero Entropy Systems