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

Department of Mathematics

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

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	495-509
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	10
Issue number	2-3
Publication status	Published - 1 Dec 2008

Keywords

Characteristic multipliers
Invariant curve
Mathieu's equation
Periodic orbit
Rigid body dynamics
Steklov periodic orbit

Cite this

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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.",

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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

Abstract

Keywords

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Cite this

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