Horseshoe map
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the square, then stretching the result into a long strip, and finally folding the strip into the shape of a horseshoe. The squishing, stretching and folding of the horseshoe map are typical of chaotic systems, but not necessary or even sufficient.
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AttractorAxiom ABaker's mapChaos theoryDynamical systemErgodicityHomoclinic connectionHomoclinic orbitHorseshoe (disambiguation)Hénon mapIndecomposable continuumIndex of fractal-related articlesList of chaotic mapsList of dynamical systems and differential equations topicsMelnikov distanceMixing (mathematics)Scientific phenomena named after peopleSmale's horseshoeSmale's horseshoe mapSmale horseshoeSmale horseshoe mapStellar pulsationStephen SmaleUshiki's theorem
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Horseshoe map
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the square, then stretching the result into a long strip, and finally folding the strip into the shape of a horseshoe. The squishing, stretching and folding of the horseshoe map are typical of chaotic systems, but not necessary or even sufficient.
has abstract
In the mathematics of chaos th ...... s a point of a periodic orbit.
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L'application fer à cheval est ...... il existe un point périodique.
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Nella teoria del caos, una map ...... forma di un ferro di cavallo.
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Podkowa Smale'a (odwzorowanie ...... atraktora w matematyce chaosu.
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Подкова Смейла — предложенный ...... олических динамических систем.
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Підкова Смейла — приклад динам ...... ткові умови покидають квадрат.
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馬蹄形写像(ばていけいしゃぞう、英語:horseshoe m ...... が横断的に交わるホモクリニック点を持つとき、馬蹄が存在する。
@ja
马蹄映射(英語:horseshoe map)在混沌理论中是指 ...... 性质具有混沌现象的各种典型特征,是混沌动力系统中的经典模型。
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title
Smale Horseshoe
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urlname
Smale_Horseshoe
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wikiPageUsesTemplate
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comment
In the mathematics of chaos th ...... necessary or even sufficient.
@en
L'application fer à cheval est ...... lles de cette dynamique sont :
@fr
Nella teoria del caos, una map ...... forma di un ferro di cavallo.
@it
Podkowa Smale'a (odwzorowanie ...... haosu, nie miałyby racji bytu.
@pl
Подкова Смейла — предложенный ...... олических динамических систем.
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Підкова Смейла — приклад динам ...... залишається поза цією областю.
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馬蹄形写像(ばていけいしゃぞう、英語:horseshoe m ...... が横断的に交わるホモクリニック点を持つとき、馬蹄が存在する。
@ja
马蹄映射(英語:horseshoe map)在混沌理论中是指 ...... 性质具有混沌现象的各种典型特征,是混沌动力系统中的经典模型。
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label
Fer à cheval de Smale
@fr
Horseshoe map
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Hufeisen-Abbildung
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Mappa a ferro di cavallo
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Podkowa Smale’a
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Подкова Смейла
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Підкова Смейла
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馬蹄形写像
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马蹄映射
@zh