Periodic orbits and non-existence of C1 first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in R4

In this paper we investigate a particular case of a zero-Hopf bifurcation of a four dimensional analytic differential system. We prove that at most five periodic orbits bifurcate from the zero-Hopf equilibrium using the averaging theory of first order and give a specific example to illustrate this c...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Tian, Renhao
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:307724
Acceso en línea:https://ddd.uab.cat/record/307724
https://dx.doi.org/urn:doi:10.1007/s12215-024-01074-8
Access Level:acceso abierto
Palabra clave:Analytic differential systems
Zero-Hopf bifurcation
Periodic orbits
Characteristic multipliers
Non-existence of C1 first integral
Descripción
Sumario:In this paper we investigate a particular case of a zero-Hopf bifurcation of a four dimensional analytic differential system. We prove that at most five periodic orbits bifurcate from the zero-Hopf equilibrium using the averaging theory of first order and give a specific example to illustrate this conclusion. Moreover we prove the non-existence of C first integrals in a neighbourhood of these periodic orbits.