On the stability of periodic orbits for differential systems in $\mathbb{R}^n$
Armengol Gasull Héctor Giacomini Maite Grau
Discrete & Continuous Dynamical Systems - B 2008, 10(2&3, September): 495-509 doi: 10.3934/dcdsb.2008.10.495
We consider an autonomous differential system in $\mathbb{R}^n$ 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: rigid body dynamics Periodic orbit characteristic multipliers Steklov periodic orbit. invariant curve Mathieu's equation

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