Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems
In this paper we study generalized Poincar´e-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in n-dimensional manifolds satisfying some suitable conditions. This result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the ge...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/72026 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/72026 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.163 Hopf bifurcation Attractor Bosuk’s homotopy Topología 1210 Topología |
| Sumario: | In this paper we study generalized Poincar´e-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in n-dimensional manifolds satisfying some suitable conditions. This result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the general case and other attractors in low dimensional manifolds. Topological techniques based on the notion of concentricity of manifolds play a substantial role in the paper. |
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