dc.contributor.author |
Llibre, Jaume |
|
dc.contributor.author |
Ponce, Enrique |
|
dc.contributor.author |
Teruel, Antonio E. |
|
dc.date.accessioned |
2020-02-12T08:42:10Z |
|
dc.date.available |
2020-02-12T08:42:10Z |
|
dc.identifier.uri |
http://hdl.handle.net/11201/150863 |
|
dc.description.abstract |
[eng] For a three-parametric family of continuous piecewise linear differential systems introduced by Arneodo et al. [1981] and considering a situation which is reminiscent of the Hopf-Zero bifurcation, an analytical proof on the existence of a two-parametric family of homoclinic orbits is provided. These homoclinic orbits exist both under Shil'nikov (0 < δ < 1) and non-Shil'nikov assumptions (δ ≥ 1). As it is well known for the case of differentiable systems, under Shil'nikov assumptions there exist infinitely many periodic orbits accumulating to the homoclinic loop. We also prove that this behavior persists at δ = 1. Moreover, for δ > 1 and sufficiently close to 1 we show that these periodic orbits persist but then they do not accumulate to the homoclinic orbit. |
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dc.format |
application/pdf |
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dc.relation.isformatof |
Versió postprint del document publicat a: https://doi.org/10.1142/S0218127407017756 |
|
dc.relation.ispartof |
International Journal of Bifurcation and Chaos, 2004, vol. 17, num. 4, p. 1171-1184 |
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dc.subject.classification |
51 - Matemàtiques |
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dc.subject.classification |
004 - Informàtica |
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dc.subject.other |
51 - Mathematics |
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dc.subject.other |
004 - Computer Science and Technology. Computing. Data processing |
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dc.title |
Horseshoes near homoclinic orbits for piecewise linear differential systems in R^3 |
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dc.type |
info:eu-repo/semantics/article |
|
dc.type |
info:eu-repo/semantics/acceptedVersion |
|
dc.date.updated |
2020-02-12T08:42:10Z |
|
dc.rights.accessRights |
info:eu-repo/semantics/openAccess |
|
dc.identifier.doi |
https://doi.org/10.1142/S0218127407017756 |
|