ON INVARIANT ε-SCRAMBLED SETS

DOI10.1142/S0218127410027465zbMath1202.37016OpenAlexW2035674632MaRDI QIDQ3065798

Piotr Oprocha, Francisco Balibrea, Juan Luis García Guirao

Publication date: 6 January 2011

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127410027465

zbMATH Keywords

topological mixingLi-Yorke chaosscrambled setsubshiftproximal relationMycielski sets

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Symbolic dynamics (37B10) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (4)

Invariant scrambled sets, uniform rigidity and weak mixing ⋮ Cardinalities of scrambled sets and positive scrambled sets ⋮ A dynamical version of the Kuratowski–Mycielski theorem and invariant chaotic sets ⋮ Recent development of chaos theory in topological dynamics

Cites Work

• Topological dynamics of transformations induced on the space of probability measures
• Horseshoes, entropy and periods for graph maps
• Topological mapping properties defined by digraphs
• There are no chaotic mappings with residual scrambled sets
• Period Three Implies Chaos
• Regular periodic decompositions for topologically transitive maps
• Li–Yorke sensitivity
• Devaney’s chaos implies existence of 𝑠-scrambled sets
• On the invariance of Li–Yorke chaos of interval maps
• Topological size of scrambled sets
• Devaney's chaos or 2-scattering implies Li-Yorke's chaos

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