Global dynamics of mechanical systems with cubic potentials
- 48 Downloads
We study the behavior of solutions of mechanical systems with polynomial potentials of degree 3 by using a blow up of McGehee type. We first state some general properties for positive degree homogeneous potentials. In particular, we prove a very general property of transversality of the invariant manifolds of the flow along the homothetic orbit. The paper focuses in the study of global flow in the case of homogeneous polynomial potentials of degree 3 for negative energy. The flow is fairly simple because of its gradient-like structure, although for some values of the polynomial coefficients we have diverse behaviour of the separatrices on the infinity manifold, which are essential to describe the global flow.
Key WordsHamiltonian Vector Field Homogeneous Polynomial Potentials Invariant Manifolds Global Flow
Unable to display preview. Download preview PDF.
- 1.J. Delgado-Fernández and E. Pérez-chavela,The rhomboidal four body problem. Global solution on the total collision Manifold in T. Ratiu, (ed.), The Geometry of Hamiltonian Systems, Springer-Verlag (1991), 97–110.Google Scholar
- 2.F.N. Diacu,On the validity of Mücket-Treder gravitational law, in E. Lacomba and J. Llibre, (eds.), New trends in Hamiltonian Systems and Celestial Mechanics, World Scientific Publ., Singapore (1995), 127–139.Google Scholar
- 3.F.N. Diacu,Collision/ejection dynamics for particle systems with quasihomogeneous potentials, (To appear)Google Scholar
- 4.M. Falconi,Estudio asintótico de escapes en sistemas Hamiltonianos Polinomiales. P.H. Dissertation, UNAM (1996).Google Scholar