CONTINUOUS BILLIARDS AND THE WEAKLY DISSIPATIVE KOLMOGOROV - ARNOLD - MOSER THEORY

摘要

Within the framework of the simplest model of the weakly dissipative Kolmogorov-Arnold-Moser theory, known as the Bogdanov-map, we compute two families of phase portraits of vector fields. These phase curves describe the moving boundary in the varia-tional problem governing a piecewise linear motion of a test particle in an inhomogeneous continuous medium.