Periodic orbits near equilibria

Luis Barreira; Jaume Llibre; Claudia Valls

doi:10.1002/cpa.20324

Periodic orbits near equilibria

Luis Barreira, Jaume Llibre, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

Lyapunov,Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc.

Original language	English
Pages (from-to)	1225-1236
Journal	Communications on Pure and Applied Mathematics
Volume	63
DOIs	https://doi.org/10.1002/cpa.20324
Publication status	Published - 1 Sept 2010

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10.1002/cpa.20324

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title = "Periodic orbits near equilibria",

abstract = "Lyapunov,Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. {\textcopyright} 2010 Wiley Periodicals, Inc.",

author = "Luis Barreira and Jaume Llibre and Claudia Valls",

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T1 - Periodic orbits near equilibria

AU - Barreira, Luis

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2010/9/1

Y1 - 2010/9/1

N2 - Lyapunov,Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc.

AB - Lyapunov,Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc.

U2 - 10.1002/cpa.20324

DO - 10.1002/cpa.20324

M3 - Article

SN - 0010-3640

VL - 63

SP - 1225

EP - 1236

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

ER -

Periodic orbits near equilibria

Abstract

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