Jp. Ortega et Ts. Ratiu, A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems, J GEOM PHYS, 32(2), 1999, pp. 131-159
The classical Dirichlet criterion on the stability of equilibria in Hamilto
nian systems is generalized to the orbital stability of periodic orbits. Th
e result obtained is adapted to the study of the stability of relative peri
odic orbits in Hamiltonian systems with symmetry that lie at regular level
sets of the corresponding momentum map. (C) 1999 Elsevier Science B.V. All
right reserved. Subj. Class.: Dynamical systems 1991 MSG: 34D35; 58F05.