Homoclinic and heteroclinic solutions for a class of two dimensional Hamiltonian systems

摘要

The problem of the existence of homoclinic and heteroclinic solutions for a class of two dimensional Hamiltonian systems, culled canyon-like, is discussed. Some basic properties, that are helpful in the qualitative analysis of dynamics, are discussed before stating the principal existence properties for the scparatrix solutions. A schematic representation of the dynamics useful for obtaining an immediate sketch of the phase portrait and in computer applications, is proposed. It has been shown how the 1 d.o.f. conservative mechanical systems have a canonical canyon-like structure.