Furstenberg families and sensitivity

DOI10.1155/2010/649348zbMath1187.37016OpenAlexW1975136850WikidataQ58650856 ScholiaQ58650856MaRDI QIDQ965764

Feng Tan, Huoyun Wang, Jin Cheng Xiong

Publication date: 26 April 2010

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/223272

zbMATH Keywords

sensitivitysymbolic dynamicsFurstenberg families

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Topological properties of mappings on manifolds (58K15) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (15)

Measure-Theoretical Sensitivity and Scrambled Sets Via Furstenberg Families ⋮ Devaney chaos and stronger forms of sensitivity on the product of semiflows ⋮ \( \mathscr{F} \)-equicontinuity and an analogue of Auslander-Yorke dichotomy theorem ⋮ On A Class Between Devaney Chaotic and Li-Yorke Chaotic Generalized Shift Dynamical Systems ⋮ Shifts, rotations and distributional chaos ⋮ Auslander-Yorke type dichotomy theorems for stronger versions of $r$-sensitivity ⋮ A note on ℱ-sensitivity for non-autonomous systems ⋮ Transitivity and sensitivity of iterated function systems via Furstenberg families ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Furstenberg families and chaos on uniform limit maps ⋮ About two definitions of \(\mathscr{F}\)-sensitivity ⋮ Stronger forms of transitivity and sensitivity for nonautonomous discrete dynamical systems and Furstenberg families ⋮ Measure-Theoretical Sensitivity and Scrambled Sets via Furstenberg Families ⋮ Thickly syndetical sensitivity of topological dynamical system ⋮ Recent development of chaos theory in topological dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Chaos via Furstenberg family couple
• Sensitive dependence to initial conditions for one dimensional maps
• Interval maps, factors of maps, and chaos
• Morse-Smale singularities in simple mechanical systems
• On Lyapunov exponent and sensitivity.
• Furstenberg family and chaos
• Proximity and distality via Furstenberg families
• Period Three Implies Chaos
• Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval
• Li–Yorke sensitivity
• On Li-Yorke pairs
• Mixing and proximal cells along sequences
• Devaney's chaos or 2-scattering implies Li-Yorke's chaos

This page was built for publication: Furstenberg families and sensitivity