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Tubular neighborhoods and continuation of Morse decompositions

Published online by Cambridge University Press:  03 July 2014

M. C. CARBINATTO  and
K. P. RYBAKOWSKI
M. C. CARBINATTO
Affiliation:
Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13.560-970 São Carlos SP, Brazil email mdccarbi@icmc.usp.br
K. P. RYBAKOWSKI
Affiliation:
Universität Rostock, Institut für Mathematik, Ulmenstrasse 69, Haus 3, 18057 Rostock, Germany email krzysztof.rybakowski@uni-rostock.de
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Abstract

We prove a continuation result for Morse decompositions under tubular singular semiflow perturbations, which generalizes a corresponding result from Carbinatto and Rybakowski [Morse decompositions in the absence of uniqueness, II. Topol. Methods Nonlinear Anal.22 (2003), 15–51] and is applicable to cases in which the phase space of the perturbed semiflow is not necessarily homeomorphic to a product of metric spaces having as a factor the phase space of the limiting semiflow. We apply this result to singularly perturbed second-order differential equations on differential manifolds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2053 - 2079
Copyright
© Cambridge University Press, 2014 

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