Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclin...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/121505 |
| Acceso en línea: | https://hdl.handle.net/2117/121505 https://dx.doi.org/10.3934/dcds.2018196 |
| Access Level: | acceso abierto |
| Palabra clave: | Dynamics Differential equations Newhouse phenomenon homoclinic and heteroclinic tangencies reversible mixed dynamics. Sistemes dinàmics Equacions diferencials Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations related to the birth of asymptotically stable, unstable and elliptic periodic orbits. |
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