Journal of Nonlinear Science

, Volume 9, Issue 5, pp 525–573

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

Cite this article as:
Shashkov, M. & Turaev, D. J. Nonlinear Sci. (1999) 9: 525. doi:10.1007/s003329900078


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.

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • M. V. Shashkov
    • 1
  • D. V. Turaev
    • 2
  1. 1.Department of Differential Equations, Institute for Applied Mathematics and Cybernetics, 10 Uljanova Street, Nizhny Novgorod 603005, RussiaRU
  2. 2.The Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, Berlin 10117, GermanyDE