Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds
In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter ???? connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on ????. The e...
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ftunivic:oai:dspace.uvic.cat:10854/2214 2023-05-15T17:39:52+02:00 Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds Corbera Subirana, Montserrat Llibre, Jaume Teixeira, Marco Antonio Universitat de Vic. Escola Politècnica Superior Universitat de Vic. Grup de Recerca en Tecnologies Digitals 2009 application/pdf http://hdl.handle.net/10854/2214 https://doi.org/10.1016/j.physd.2009.01.002 eng eng Elsevier http://www.sciencedirect.com/science/article/pii/S0167278909000049 CORBERA SUBIRANA, Montserrat; LLIBRE, Jaume; ANTONIO TEIXEIRA, Marco. "Symmetric periodic orbits near a heteroclinic loop in R-3 formed by two singular points, a semistable periodic orbit and their invariant manifolds". A: Physica D-Nonlinear Phenomena, 2009, vol. 238, núm. 6, pàg. 699-705. 0167-2789 http://hdl.handle.net/10854/2214 https://doi.org/10.1016/j.physd.2009.01.002 (c) Elsevier Tots els drets reservats info:eu-repo/semantics/openAccess Matemàtica info:eu-repo/semantics/article info:eu-repo/acceptedVersion 2009 ftunivic https://doi.org/10.1016/j.physd.2009.01.002 2022-06-06T18:09:09Z In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter ???? connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on ????. The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics. Article in Journal/Newspaper North Pole South pole Universitat de Vic: RIUVic North Pole South Pole Physica D: Nonlinear Phenomena 238 6 699 705 |
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Matemàtica |
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Matemàtica Corbera Subirana, Montserrat Llibre, Jaume Teixeira, Marco Antonio Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
topic_facet |
Matemàtica |
description |
In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter ???? connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on ????. The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics. |
author2 |
Universitat de Vic. Escola Politècnica Superior Universitat de Vic. Grup de Recerca en Tecnologies Digitals |
format |
Article in Journal/Newspaper |
author |
Corbera Subirana, Montserrat Llibre, Jaume Teixeira, Marco Antonio |
author_facet |
Corbera Subirana, Montserrat Llibre, Jaume Teixeira, Marco Antonio |
author_sort |
Corbera Subirana, Montserrat |
title |
Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
title_short |
Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
title_full |
Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
title_fullStr |
Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
title_full_unstemmed |
Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
title_sort |
symmetric periodic orbits near a heteroclinic loop in r3 formed by two singular points, a semistable periodic orbit and their invariant manifolds |
publisher |
Elsevier |
publishDate |
2009 |
url |
http://hdl.handle.net/10854/2214 https://doi.org/10.1016/j.physd.2009.01.002 |
geographic |
North Pole South Pole |
geographic_facet |
North Pole South Pole |
genre |
North Pole South pole |
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North Pole South pole |
op_relation |
http://www.sciencedirect.com/science/article/pii/S0167278909000049 CORBERA SUBIRANA, Montserrat; LLIBRE, Jaume; ANTONIO TEIXEIRA, Marco. "Symmetric periodic orbits near a heteroclinic loop in R-3 formed by two singular points, a semistable periodic orbit and their invariant manifolds". A: Physica D-Nonlinear Phenomena, 2009, vol. 238, núm. 6, pàg. 699-705. 0167-2789 http://hdl.handle.net/10854/2214 https://doi.org/10.1016/j.physd.2009.01.002 |
op_rights |
(c) Elsevier Tots els drets reservats info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1016/j.physd.2009.01.002 |
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Physica D: Nonlinear Phenomena |
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6 |
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