Structures in the phase space of a four dimensional symplectic map
There are a lot of scientists interested in equivalently Hamiltonian systems of two degrees of freedom, also called two-dimensional symplectic maps \((2-\Delta)\), but there are just a few who successfully investigated the behavior of higher dimensional systems. Among htese are the authors of the present paper. They consider that it is of high interest to find the types of structures that exist in a \(4-\Delta\) phase space. Therefore, the authors numerically investigate the projections of nonperiodic orbits in a \(4-\Delta\) symplectic map composed of two-coupled \(2-\Delta\) maps. They also give a detailed description of the structures that are produced in different planes of projection and they find how the morphology of the \(4-\Delta\) orbits is influenced by the featues of the \(2-\Delta\) maps when the coupling parameter increases. Moreover, the authors succeed to give an empirical law that describes this influence. Briefly, the main result of the paper consists in the fact that the \(2-\Delta\) maps strongly influence the \(4-\Delta\) case and the existence of well defined structures in the projections of the \(2-\Delta\) tori.
scientific article; zbMATH DE number 1051297