Continuous billiards and the weakly dissipative Kolmogorov – Arnold – Moser theory

Abstract

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 variational problem governing a piecewise linear motion of a test particle in an inhomogeneous continuous medium. Bibliography: 6 titles. Illustrations: 1 figure.