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Generation of homoclinic tangencies by $C^1$-perturbations.
| hal.structure.identifier | Institut de Mathématiques de Bourgogne [Dijon] [IMB] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GOURMELON, Nicolas | |
| dc.date.accessioned | 2024-04-04T02:28:56Z | |
| dc.date.available | 2024-04-04T02:28:56Z | |
| dc.date.created | 2009 | |
| dc.date.issued | 2010 | |
| dc.identifier.issn | 1078-0947 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190133 | |
| dc.description.abstractEn | Given a [C^1] -diffeomorphism [f] of a compact manifold, we show that if the stable/unstable dominated splitting along a saddle is weak enough, then there is a small [C^1] -perturbation that preserves the orbit of the saddle and that generates a homoclinic tangency related to it. Moreover, we show that the perturbation can be performed preserving a homoclinic relation to another saddle. We derive some consequences on homoclinic classes. In particular, if the homoclinic class of a saddle [P] has no dominated splitting of same index as [P] , then a [C^1] -perturbation generates a homoclinic tangency related to [P] . | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.subject.en | Dominated splitting | |
| dc.subject.en | homoclinic tangency | |
| dc.subject.en | bifurcation | |
| dc.subject.en | homoclinic class. | |
| dc.subject.en | homoclinic class | |
| dc.title.en | Generation of homoclinic tangencies by $C^1$-perturbations. | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.3934/dcds.2010.26.1 | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| bordeaux.journal | Discrete and Continuous Dynamical Systems - Series A | |
| bordeaux.page | 1-42 | |
| bordeaux.volume | 26 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00489042 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00489042v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Discrete%20and%20Continuous%20Dynamical%20Systems%20-%20Series%20A&rft.date=2010&rft.volume=26&rft.issue=1&rft.spage=1-42&rft.epage=1-42&rft.eissn=1078-0947&rft.issn=1078-0947&rft.au=GOURMELON,%20Nicolas&rft.genre=article |
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