About: Morse–Smale system

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In dynamical systems theory, an area of pure mathematics, a Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition on the stable and unstable manifolds. Morse–Smale systems are structurally stable and form one of the simplest and best studied classes of smooth dynamical systems. They are named after Marston Morse, the creator of the Morse theory, and Stephen Smale, who emphasized their importance for smooth dynamics and algebraic topology.

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rdfs:label	Morse-Smale-System (de) Morse–Smale system (en)
rdfs:comment	In der Theorie der dynamischen Systeme lassen sich verschiedene Flüsse und dynamische Systeme unter dem Begriff der Morse-Smale-Systeme zusammenfassen. Morse-Smale-Systeme sind strukturell stabil, d. h. ihr qualitatives Verhalten ändert sich nicht unter geringfügigen Störungen der Parameter. (de) In dynamical systems theory, an area of pure mathematics, a Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition on the stable and unstable manifolds. Morse–Smale systems are structurally stable and form one of the simplest and best studied classes of smooth dynamical systems. They are named after Marston Morse, the creator of the Morse theory, and Stephen Smale, who emphasized their importance for smooth dynamics and algebraic topology. (en)
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dcterms:subject	Dynamical systems
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Wikipage revision ID	1073415656 (xsd:integer)
Link from a Wikipage to another Wikipage	Non-wandering set Algebraic topology Dynamical systems theory Compact space Critical point (mathematics) Morse theory Stephen Smale Peixoto's theorem Structural stability Flow (mathematics) Gradient-like dynamical systems Riemannian manifold Hyperbolic equilibrium point Hyperbolic set Dynamical systems Manifold Marston Morse Stable manifold Pure mathematics Separatrix (dynamical systems) Morse function Unstable manifold Periodic orbit
sameAs	Morse–Smale system Morse–Smale system Morse–Smale system Morse–Smale system
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thumbnail	wiki-commons:Special:FilePath/UprightTorusFlowLines.png?width=300
curator	Dr. Michael Shub (en)
author	D. V. Anosov (en)
id	M/m064990 (en)
title	Morse–Smale system (en) Morse-Smale systems (en)
urlname	Morse-Smale_systems (en)
has abstract	In der Theorie der dynamischen Systeme lassen sich verschiedene Flüsse und dynamische Systeme unter dem Begriff der Morse-Smale-Systeme zusammenfassen. Morse-Smale-Systeme sind strukturell stabil, d. h. ihr qualitatives Verhalten ändert sich nicht unter geringfügigen Störungen der Parameter. (de) In dynamical systems theory, an area of pure mathematics, a Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition on the stable and unstable manifolds. Morse–Smale systems are structurally stable and form one of the simplest and best studied classes of smooth dynamical systems. They are named after Marston Morse, the creator of the Morse theory, and Stephen Smale, who emphasized their importance for smooth dynamics and algebraic topology. (en)
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foaf:isPrimaryTopicOf	wikipedia-en:Morse–Smale_system
is Link from a Wikipage to another Wikipage of	Morse–Smale function Anosov diffeomorphism Morse-Smale function Stephen Smale Structural stability Gradient-like vector field Axiom A Morse-Smale system
is Wikipage redirect of	Morse–Smale function Morse-Smale function Morse-Smale system
is known for of	Stephen Smale
is known for of	Stephen Smale
is foaf:primaryTopic of	wikipedia-en:Morse–Smale_system

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