An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop

M. V. Shashkov; D. V. Turaev

doi:10.1007/s003329900078

An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop

M. V. Shashkov, D. V. Turaev

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

15 Scopus citations

Abstract

In this paper we give a proof of the existence of smooth nonlocal center manifolds for systems close to a system with a homoclinic orbit to a saddle-type equilibrium point. Our proof is based on a consideration of some class of the boundary value problems (see Section 3). We obtain estimates for solutions of the boundary value problems that allow us to prove the theorem on the center manifolds at the C¹ -assumptions for the smoothness of systems.

Original language	English
Pages (from-to)	525-573
Number of pages	49
Journal	Journal of Nonlinear Science
Volume	9
Issue number	5
DOIs	https://doi.org/10.1007/s003329900078
State	Published - 1 Jan 1999
Externally published	Yes

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Applied Mathematics

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10.1007/s003329900078

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title = "An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop",

abstract = "In this paper we give a proof of the existence of smooth nonlocal center manifolds for systems close to a system with a homoclinic orbit to a saddle-type equilibrium point. Our proof is based on a consideration of some class of the boundary value problems (see Section 3). We obtain estimates for solutions of the boundary value problems that allow us to prove the theorem on the center manifolds at the C1 -assumptions for the smoothness of systems.",

author = "Shashkov, {M. V.} and Turaev, {D. V.}",

note = "Funding Information: The authors are grateful to L. P. Shilnikov, V. N. Belykh, L. M. Lerman, S. V. Gonchenko, O. V. Stenkin, B. Fiedler, and A. J. Homburg for useful discussions. This research was supported by the EC-Russia Collaborative Project ESPRIT P 9282–ACTCS, by the ISF grant R98300, and the grant of INTAS-93-0570-ext. M. Shashkov was also supported by DAAD (1995) to work at Institut f{\"u}r Mathematik I, Freie Universit{\"a}t, Berlin.",

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AU - Turaev, D. V.

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N2 - In this paper we give a proof of the existence of smooth nonlocal center manifolds for systems close to a system with a homoclinic orbit to a saddle-type equilibrium point. Our proof is based on a consideration of some class of the boundary value problems (see Section 3). We obtain estimates for solutions of the boundary value problems that allow us to prove the theorem on the center manifolds at the C1 -assumptions for the smoothness of systems.

AB - In this paper we give a proof of the existence of smooth nonlocal center manifolds for systems close to a system with a homoclinic orbit to a saddle-type equilibrium point. Our proof is based on a consideration of some class of the boundary value problems (see Section 3). We obtain estimates for solutions of the boundary value problems that allow us to prove the theorem on the center manifolds at the C1 -assumptions for the smoothness of systems.

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An existence theorem of smooth nonlocal center manifolds for systems close to a system with a homoclinic loop

Abstract

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