The Closing Lemma for Generalized Recurrence in the Plane

DOI10.2307/2000955zbMath0648.34059OpenAlexW4234482084WikidataQ125025915 ScholiaQ125025915MaRDI QIDQ3793027

Maria Lúcia Alvarenga Peixoto

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2000955

zbMATH Keywords

generalized recurrenceprolongational limit sets

Mathematics Subject Classification ID

Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Ordinary differential equations and systems on manifolds (34C40) Dynamical systems and ergodic theory (37-XX)

Related Items (8)

Prolongational centers and their depths ⋮ Systems of differential equations that are competitive or cooperative. VI: A localC^rClosing Lemma for 3-dimensional systems ⋮ Closing lemmas ⋮ Is every pseudo-orbit of some homeomorphism near an exact orbit of a nearby homeomorphism? ⋮ The generalized recurrent set and strong chain recurrence ⋮ The Planar Closing Lemma for Chain Recurrence ⋮ Qualitative theory of flows on surfaces (a review) ⋮ Strengthening the \(C^r\)-closing lemma for dynamical systems and foliations on the torus

Cites Work

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• On stability of dynamical systems on open manifolds
• On an approximation theorem of Kupka and Smale
• Structurally stable systems on open manifolds are never dense
• The C¹ Closing Lemma, including Hamiltonians
• Global structural stability of flows on open surfaces
• Explosions in Completely Unstable Flows. I Preventing Explosions
• Explosions in Completely Unstable Flows. II Some Examples
• The Planar Closing Lemma for Chain Recurrence
• The Closing Lemma
• An Improved Closing Lemma and a General Density Theorem
• Sur les courbes définies par les équations différentielles dans l'espace à $m$ dimensions

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