Phase portraits of the Manev systems

摘要: The Manev systems are two {body problems dened by a potential of the form a= r+ b= r 2, where r is the distance between the two particles, and a and b are arbitrary constants. The Hamiltonian H=(p 2 r+ p 2= r 2)= 2+ a= r+ b= r 2 and the angular momemtum p= r 2 _ associated to Manev systems are two rst integrals, independent and in involution. Let I h (respectiveley I c) be the set of points of the phase space on which H (respectively p) takes the value h (respectively c). Since H and p are rst integrals, the sets I h, I c and I hc= I h