On the stability of periodic orbits for differential systems in R n

Armengol Gasull; Héctor Giacomini; Maite Grau

On the stability of periodic orbits for differential systems in R ⁿ

Armengol Gasull, Héctor Giacomini, Maite Grau

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

4 Citas (Scopus)

Resumen

We consider an autonomous differential system in ℝn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n - 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Idioma original	Inglés
Páginas (desde-hasta)	495-509
Publicación	Discrete and Continuous Dynamical Systems - Series B
Volumen	10
N.º	2-3
Estado	Publicada - 1 dic 2008

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title = "On the stability of periodic orbits for differential systems in R n",

abstract = "We consider an autonomous differential system in ℝn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n - 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.",

keywords = "Characteristic multipliers, Invariant curve, Mathieu's equation, Periodic orbit, Rigid body dynamics, Steklov periodic orbit",

author = "Armengol Gasull and H{\'e}ctor Giacomini and Maite Grau",

year = "2008",

month = dec,

day = "1",

language = "English",

volume = "10",

pages = "495--509",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

number = "2-3",

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T1 - On the stability of periodic orbits for differential systems in R n

AU - Gasull, Armengol

AU - Giacomini, Héctor

AU - Grau, Maite

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We consider an autonomous differential system in ℝn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n - 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

AB - We consider an autonomous differential system in ℝn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n - 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

KW - Characteristic multipliers

KW - Invariant curve

KW - Mathieu's equation

KW - Periodic orbit

KW - Rigid body dynamics

KW - Steklov periodic orbit

M3 - Article

SN - 1531-3492

VL - 10

SP - 495

EP - 509

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 2-3

ER -

On the stability of periodic orbits for differential systems in R n

Resumen

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On the stability of periodic orbits for differential systems in R ⁿ