Bifurcations from families of periodic solutions in piecewise differential systems

Consider a differential system of the form x'=F0(t,x)+∑ki=1εiFi(t,x)+εk+1R(t,x,ε),where Fi:S1×D → Rm and R:S1×D×(-ε0,ε0)→ Rm are piecewise Ck+1 functions and T-periodic in the variable t. Assuming that the unperturbed system x'= F0(t,x) has a d-dimensional submanifold of periodic solutions...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Novaes, Douglas D.|||0000-0002-9147-8442, Rodrigues, Camila A. B.
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221298
Acceso en línea:https://ddd.uab.cat/record/221298
https://dx.doi.org/urn:doi:10.1016/j.physd.2020.132342
Access Level:acceso abierto
Palabra clave:Lyapunov-Schmidt reduction
Periodic solution
Averaging method
Nonsmooth differential system
Piecewise smooth differential system
Descripción
Sumario:Consider a differential system of the form x'=F0(t,x)+∑ki=1εiFi(t,x)+εk+1R(t,x,ε),where Fi:S1×D → Rm and R:S1×D×(-ε0,ε0)→ Rm are piecewise Ck+1 functions and T-periodic in the variable t. Assuming that the unperturbed system x'= F0(t,x) has a d-dimensional submanifold of periodic solutions with d < m, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated T-periodic solutions of the above differential system.