TY - JOUR
T1 - Dynamics of the Morse Oscillator
T2 - Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics
AU - Krajňák, Vladimír
AU - Wiggins, Stephen
PY - 2019/10/1
Y1 - 2019/10/1
N2 - We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.
AB - We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.
KW - chaos
KW - Melnikov function
KW - homoclinic orbit
KW - action-angle variables
KW - Morse oscillator
UR - http://www.scopus.com/inward/record.url?scp=85073711372&partnerID=8YFLogxK
U2 - 10.1142/S0218127419501578
DO - 10.1142/S0218127419501578
M3 - Article (Academic Journal)
SN - 0218-1274
VL - 29
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 11
M1 - 1950157
ER -