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

Armengol Gasull, Héctor Giacomini, Maite Grau

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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 languageEnglish
Pages (from-to)495-509
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume10
Issue number2-3
Publication statusPublished - 1 Dec 2008

Keywords

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

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