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    Chaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators

    Source: Journal of Applied Mechanics:;1988:;volume( 055 ):;issue: 004::page 959
    Author:
    Stephen Wiggins
    ,
    Steven W. Shaw
    DOI: 10.1115/1.3173748
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: We present general results pertaining to chaotic motions in a class of systems termed slowly varying oscillators which consist of weakly perturbed single-degree-of-freedom systems in which parameters vary slowly in time according to an additional equation of motion. Our results include an analytical method for detecting transversal intersections of stable and unstable manifolds (typically a necessary condition for chaotic motions to exist) and a detailed description of the chaotic dynamics that occur when this situation exists.
    keyword(s): Chaos , Motion , Equations of motion , Intersections , Manifolds AND Dynamics (Mechanics) ,
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      Chaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators

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    contributor authorStephen Wiggins
    contributor authorSteven W. Shaw
    date accessioned2017-05-08T23:26:23Z
    date available2017-05-08T23:26:23Z
    date copyrightDecember, 1988
    date issued1988
    identifier issn0021-8936
    identifier otherJAMCAV-26299#959_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/103453
    description abstractWe present general results pertaining to chaotic motions in a class of systems termed slowly varying oscillators which consist of weakly perturbed single-degree-of-freedom systems in which parameters vary slowly in time according to an additional equation of motion. Our results include an analytical method for detecting transversal intersections of stable and unstable manifolds (typically a necessary condition for chaotic motions to exist) and a detailed description of the chaotic dynamics that occur when this situation exists.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleChaos and Three-Dimensional Horseshoes in Slowly Varying Oscillators
    typeJournal Paper
    journal volume55
    journal issue4
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3173748
    journal fristpage959
    journal lastpage968
    identifier eissn1528-9036
    keywordsChaos
    keywordsMotion
    keywordsEquations of motion
    keywordsIntersections
    keywordsManifolds AND Dynamics (Mechanics)
    treeJournal of Applied Mechanics:;1988:;volume( 055 ):;issue: 004
    contenttypeFulltext
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