TY - JOUR
T1 - On the periodic orbits of Hamiltonian systems
AU - Llibre, Jaume
AU - Rodrigues, Ana
PY - 2010/4/1
Y1 - 2010/4/1
N2 - We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the periodic orbits of these integrable systems, first perturbing the Hooke Hamiltonian with a nonautonomous potential, and second perturbing the Kepler problem with an autonomous potential. © 2010 American Institute of Physics.
AB - We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the periodic orbits of these integrable systems, first perturbing the Hooke Hamiltonian with a nonautonomous potential, and second perturbing the Kepler problem with an autonomous potential. © 2010 American Institute of Physics.
UR - https://ddd.uab.cat/record/226104
U2 - https://doi.org/10.1063/1.3387343
DO - https://doi.org/10.1063/1.3387343
M3 - Article
VL - 51
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
M1 - 048004JMP
ER -