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http://hdl.handle.net/1942/4040
Title: | Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle | Authors: | CAUBERGH, Magdalena DUMORTIER, Freddy Roussarie, Robert |
Issue Date: | 2007 | Publisher: | AMER INST MATHEMATICAL SCIENCES | Source: | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 6(1). p. 1-21 | Abstract: | It is known that perturbations from a Hamiltonian 2-saddle cycle F can produce limit cycles that are not covered by the Abelian integral, even when the Abelian integral is generic. These limit cycles are called alien limit cycles. In this paper, extending the results of [6] and [2], we investigate the number of alien limit cycles in generic multi-parameter rigid unfoldings of the Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. | Notes: | Univ Hasselt, B-3590 Diepenbeek, Belgium. Univ Bourgogne, CNRS, UMR 5584, IMB, F-21078 Dijon, France.Caubergh, M, Univ Hasselt, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.magdalena.caubergh@uhasselt.be freddy.dumortier@uhasselt.be roussari@mail.u-bourgogne.fr | Keywords: | planar vector field; Hamiltonian perturbation; limit cycle; Abelian integral; two-saddle cycle; asymptotic scale deformation | Document URI: | http://hdl.handle.net/1942/4040 | Link to publication/dataset: | http://aimsciences.org/journals/pdfs.jsp?paperID=2145&mode=abstract | ISSN: | 1534-0392 | e-ISSN: | 1553-5258 | ISI #: | 000243024100001 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2008 |
Appears in Collections: | Research publications |
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