About: Pugh's closing lemma

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In mathematics, Pugh's closing lemma is a result that links periodic orbit solutions of differential equations to chaotic behaviour. It can be formally stated as follows: Let be a diffeomorphism of a compact smooth manifold . Given a nonwandering point of , there exists a diffeomorphism arbitrarily close to in the topology of such that is a periodic point of .

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rdfs:label	Lema de Pugh (ca) Pughs Schließungslemma (de) Pugh's closing lemma (en)
rdfs:comment	In der Theorie dynamischer Systeme besagt Pughs Schließungslemma, dass ein dynamisches System mit nichtwandernden Punkten in der -Topologie beliebig gut durch dynamische Systeme mit periodischen Orbiten approximiert werden kann. Es wurde von Charles C. Pugh bewiesen. Es ist eine offene Frage, ob dies auch in der -Topologie gilt (10. Smalesches Problem). René Thom hatte vor Pugh einen fehlerhaften Beweis veröffentlicht (den Fehler fand Mauricio Peixoto). (de) In mathematics, Pugh's closing lemma is a result that links periodic orbit solutions of differential equations to chaotic behaviour. It can be formally stated as follows: Let be a diffeomorphism of a compact smooth manifold . Given a nonwandering point of , there exists a diffeomorphism arbitrarily close to in the topology of such that is a periodic point of . (en) En matemàtiques, el lema de Pugh és un resultat que relaciona les solucions d'òrbita periòdica de equacions diferencials amb el comportament caòtic. Es pot anunciar formalment com: Sigui un difeomorfisme d'una varietat diferenciable compacta . Donat un punt errant de , existeix un difeomorfisme arbitràriament proper a en la topologia de tal que és un de . (ca)
dct:subject	Lemmas in analysis Dynamical systems Limit sets
Wikipage page ID	14617622 (xsd:integer)
Wikipage revision ID	1049402202 (xsd:integer)
Link from a Wikipage to another Wikipage	Dynamical system Compact space Mathematics Orbit (dynamics) Smale's problems Topology Wandering set Diffeomorphism Differential equation Lemmas in analysis Dynamical systems Limit sets Chaos theory Differentiable manifold Autonomous convergence theorem Periodic point
sameAs	Pugh's closing lemma Pugh's closing lemma Pugh's closing lemma Pugh's closing lemma Pugh's closing lemma Pugh's closing lemma
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id	5526 (xsd:integer)
title	Pugh's closing lemma (en)
has abstract	En matemàtiques, el lema de Pugh és un resultat que relaciona les solucions d'òrbita periòdica de equacions diferencials amb el comportament caòtic. Es pot anunciar formalment com: Sigui un difeomorfisme d'una varietat diferenciable compacta . Donat un punt errant de , existeix un difeomorfisme arbitràriament proper a en la topologia de tal que és un de . El lema de Pugh implica, per exemple, que el conjunt caòtic en un sistema dinàmic continu fitat correspon a una òrbita periòdica en un sistema dinàmic diferent però estretament relacionat. Per tant, un conjunt obert de condicions en un sistema dinàmic continu fitat que segueix un comportament periòdic no podrà tenir un comportament caòtic. Això és la base d'alguns . (ca) In der Theorie dynamischer Systeme besagt Pughs Schließungslemma, dass ein dynamisches System mit nichtwandernden Punkten in der -Topologie beliebig gut durch dynamische Systeme mit periodischen Orbiten approximiert werden kann. Es wurde von Charles C. Pugh bewiesen. Es ist eine offene Frage, ob dies auch in der -Topologie gilt (10. Smalesches Problem). René Thom hatte vor Pugh einen fehlerhaften Beweis veröffentlicht (den Fehler fand Mauricio Peixoto). (de) In mathematics, Pugh's closing lemma is a result that links periodic orbit solutions of differential equations to chaotic behaviour. It can be formally stated as follows: Let be a diffeomorphism of a compact smooth manifold . Given a nonwandering point of , there exists a diffeomorphism arbitrarily close to in the topology of such that is a periodic point of . (en)
prov:wasDerivedFrom	wikipedia-en:Pugh's_closing_lemma?oldid=1049402202&ns=0
page length (characters) of wiki page	1923 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Pugh's_closing_lemma
is Link from a Wikipage to another Wikipage of	List of lemmas Smale's problems Charles C. Pugh Autonomous convergence theorem Smale's tenth problem
is Wikipage redirect of	Smale's tenth problem
is foaf:primaryTopic of	wikipedia-en:Pugh's_closing_lemma

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