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...

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Detalles Bibliográficos
Autores: Barge, Héctor, Sanjurjo, José M. R.
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
Descripción
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.