Attractors and chain recurrence for semigroup actions

DOI10.1007/s10884-010-9164-3zbMath1209.37013OpenAlexW2040544628MaRDI QIDQ616196

Josiney A. Souza, Carlos José Braga Barros

Publication date: 7 January 2011

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-010-9164-3

zbMATH Keywords

attractorslimit setschain recurrencecomplementary repellers

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35)

Related Items (38)

Lyapunov stability on fiber bundles ⋮ A note on Poincaré recurrence for semigroup actions via Furstenberg family ⋮ Semigroup actions under compactifications: a view from control systems ⋮ Attraction and Lyapunov stability for control systems on vector bundles ⋮ Cantor-Kuratowski theorem in admissible spaces ⋮ On chain recurrence for bitransformation semigroups ⋮ Chain recurrence in \(\beta \)-compactifications of topological groups ⋮ Lyapunov stability and weak attraction for control systems ⋮ Unnamed Item ⋮ Finest Morse decompositions for semigroup actions on fiber bundles ⋮ Entropy for semigroup actions on general topological spaces ⋮ Complete Lyapunov functions of control systems ⋮ Morse decompositions of topological cocycles ⋮ Recurrence theorem for semigroup actions ⋮ Attractors and chain recurrence for semigroup of continuous maps ⋮ \(M\)-systems and scattering systems of semigroup actions ⋮ Dynamic Morse decompositions for semigroups of homeomorphisms and control systems ⋮ Lyapunov stability for semigroup actions ⋮ Some aspects of stability for semigroup actions and control systems ⋮ Algebraic description of chain transitivity for semigroup actions on flag bundles ⋮ Hyperconvergence in topological dynamics ⋮ On limit behavior of skew-product transformation semigroups ⋮ Chain transitivity for semigroup actions on flag bundles ⋮ On the number of maximal chain transitive sets in fiber bundles ⋮ Topological properties of prolongations and stable sets for semigroup actions ⋮ Global attractors for semigroup actions ⋮ LEBESGUE COVERING LEMMA ON NONMETRIC SPACES ⋮ On Morse decompositions of control systems ⋮ Characterization of uniform attractors for control systems ⋮ Global attractors for semigroup actions on uniformizable spaces ⋮ On attractors and stability for semigroup actions and control systems ⋮ Force recurrence of semigroup actions ⋮ On limit behavior of semigroup actions on noncompact spaces ⋮ Unnamed Item ⋮ A characterization of completely regular spaces ⋮ Existence and uniqueness for directional attractors of topological cocycles ⋮ Attraction, Lyapunov stability and orbital maps for semigroup actions on topological spaces and fiber bundles ⋮ Topological bifurcations of minimal invariant sets for set-valued dynamical systems

Cites Work

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• Chain control sets for semigroup actions
• Linear control semigroups acting on projective space
• Existence of dichotomies and invariant splittings for linear differential systems. II
• Semiflows on topological spaces: chain transitivity and semigroups
• Morse decomposition of semiflows on topological spaces
• Morse decomposition of semiflows on fiber bundles
• The topological dynamics of semigroup actions
• Chain transitive sets for flows on flag bundles
• Maximal subsemigroups of Lie groups that are total
• The gradient structure of a flow: I
• The dynamics of control. With an appendix by Lars Grüne

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