Publicación: PERIODIC SOLUTIONS IN A 2D-SYMMETRIC HAMILTONIAN SYSTEM THROUGH REDUCTION AND AVERAGING METHOD
Fecha
2024
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DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL
Resumen
WE STUDY A TYPE OF PERTURBED POLYNOMIAL HAMILTONIAN SYSTEM IN 1:1 RESONANCE. THE PERTURBATION CONSISTS OF A HOMOGENEOUS QUARTIC POTENTIAL INVARIANT BY ROTATIONS OF ?/2 RADIANS. THE EXISTENCE OF PERIODIC SOLUTIONS IS ESTABLISHED USING REDUCTION AND AVERAGING THEORIES.
THE DIFFERENT TYPES OF PERIODIC SOLUTIONS, LINEAR STABILITY, AND BIFUR-
CATION CURVES ARE CHARACTERIZED IN TERMS OF THE PARAMETERS. FINALLY,
SOME CHOREOGRAPHY OF BIFURCATIONS ARE OBTAINED, SHOWING IN DETAIL THE EVOLUTION OF THE PHASE FLOW.
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Resonant Hamiltonians and 1:1 resonance, Reeb?s theorem, periodic solutions and linear stability, normalisation and reduction, averaging
