Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/1560
Title: Asymptotic phase and invariant foliations near periodic orbits
Authors: DUMORTIER, Freddy 
Issue Date: 2006
Publisher: American Mathematical Society
Source: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134(10). p. 2989-2996
Abstract: The paper deals with asymptotic phase and invariant foliations near periodic orbits, extending for two-dimensional smooth vector fields results that have been obtained by Chicone and Liu (2004). The problem of the existence of asymptotic phase is completely solved for analytic vector fields and is reduced to a problem of infinite codimension for C infinity systems. Moreover it is proven that whenever asymptotic phase occurs, or in other words, when the periodic orbit is isochronous, then there also exists a C infinity foliation, with leaves transversally cutting the periodic orbit and invariant under the flow of the vector field. The paper also provides some results in three dimensions.
Keywords: periodic orbit; asymptotic phase; isochronous; invariant foliations;; Poincare map; return-time map
Document URI: http://hdl.handle.net/1942/1560
ISSN: 0002-9939
e-ISSN: 1088-6826
DOI: 10.1090/S0002-9939-06-08392-4
ISI #: 000238321100026
Category: A1
Type: Journal Contribution
Validations: ecoom 2007
Appears in Collections:Research publications

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