Consider the two-degrees-of-freedom Hamiltonian given by H(p, q) = 1 2 (p2 1 + q2 1 )

Consider the two-degrees-of-freedom Hamiltonian given by H(p, q) =

ω1 2

(p2 1 + q2 1 ) +

ω2 2

(p2 2 + q2 2 ).

Plot three-dimensional and two-dimensional Poincaré sections when

(a) ω1 = 3 and ω2 = 7 for the set of initial conditions t = 0, p1 = 0.5, p2 = 1.5, q1 = 0.5, q2 = 0,

(b) ω1 = √2 and ω2 = 3 for the set of initial conditions t = 0, p1 = 0.5, p2 = 1.5, q1 = 0.5, q2 = 0.