Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems

Shui Nee Chow; Bo Deng

doi:10.1090/S0002-9947-1989-0988882-6

Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems

Shui Nee Chow, Bo Deng

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Under some generic conditions, we show how a unique stable periodic orbit can bifurcate from a homoclinic orbit for semilinear parabolic equations and retarded functional differential equations. This is a generalization of a result of Sil'nikov for ordinary differential equations.

Original language	English (US)
Pages (from-to)	539-587
Number of pages	49
Journal	Transactions of the American Mathematical Society
Volume	312
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1989-0988882-6
State	Published - Apr 1989

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1989-0988882-6

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title = "Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems",

abstract = "Under some generic conditions, we show how a unique stable periodic orbit can bifurcate from a homoclinic orbit for semilinear parabolic equations and retarded functional differential equations. This is a generalization of a result of Sil'nikov for ordinary differential equations.",

author = "Chow, {Shui Nee} and Bo Deng",

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AU - Chow, Shui Nee

AU - Deng, Bo

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N2 - Under some generic conditions, we show how a unique stable periodic orbit can bifurcate from a homoclinic orbit for semilinear parabolic equations and retarded functional differential equations. This is a generalization of a result of Sil'nikov for ordinary differential equations.

AB - Under some generic conditions, we show how a unique stable periodic orbit can bifurcate from a homoclinic orbit for semilinear parabolic equations and retarded functional differential equations. This is a generalization of a result of Sil'nikov for ordinary differential equations.

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Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems

Abstract

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