On the Appearance of Mixed Dynamics as a Result of Collision of Strange Attractors and Repellers in Reversible Systems

Abstract

In this work, we propose a scenario of appearance of mixed dynamics in reversible two-dimensional diffeomorphisms. A jump-like increase in the sizes of the strange attractor and strange repeller, which is due to the heteroclinic intersections of the invariant manifolds of the saddle points belonging to the attractor and the repeller, is the key point of the scenario. Such heteroclinic intersections appear immediately after the collisions of the strange attractor and the strange repeller with the boundaries of their attraction and repulsion basins, respectively, after which the attractor and the repeller intersect. Then the dissipative chaotic dynamics related to the existence of the mutually separable strange attractor and strange repeller immediately becomes mixed when the attractor and the repeller are essentially inseparable. The possibility of realizing the proposed scenario is demonstrated using a well-known problem of the rigid-body dynamics, namely, the nonholonomic model of the Suslov top.