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  • О возникновении смешанной динамики в результате столкновения странных аттракторов и репеллеров в обратимых системах

Article

О возникновении смешанной динамики в результате столкновения странных аттракторов и репеллеров в обратимых системах

In this paper, a new scenario of the appearance of mixed dynamics in two-dimensional reversible diffeomorphisms is proposed. The key point of the scenario is a sharp increase of the sizes of both strange attractor and strange repeller which appears due to heteroclinic bifurcations of the invariant manifolds of saddle fixed points belonging to these attractor and repeller. Due to such bifurcations, a strange attractor collides with the boundary of its absorbing domain, while a strange repeller collides with the boundary of it's ``repulsion'' domain and, as a result, the intersections between these two sets appear immediately. As a result of the scenario, the dissipative dynamics associated with the existence of strange attractor and strange repeller (which are separated from each other) sharply becomes mixed, when attractors and repellers are principally inseparable. The possibility of implementing the proposed scenario is demonstrated on the example of such a well-known problem from rigid body dynamics as a nonholonomic model of Suslov top.