On the Appearance of Mixed Dynamics as a Result of Collision of Strange Attractors and Repellers in Reversible Systems
- 10 Downloads
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.
Unable to display preview. Download preview PDF.
- 1.C. Conley, in: CBMS Regional Conf. Series in Mathematics, Vol. 38, American Mathematical Society, Providence, RI (1978), p. 89.Google Scholar
- 4.S. V. Gonchenko and D. V. Turaev, in: Proc. V. A. Steklov Math. Inst. Rus. Acad. Sci., 297, 133 (2017).Google Scholar
- 5.S. V. Gonchenko, D. V. Turaev, and L. P. Shil’nikov, in: Proc. V. A. Steklov Math. Inst. Rus. Acad. Sci., 216, 76 (1997).Google Scholar
- 11.D. V. Anosov and I. U. Bronshtein, “Smooth dynamical systems, Ch. 3, Topologic dynamics,” in: Itogi Nauki Tekhn., Ser. Probl. Mat. Fund. Napr., 1, 204 (1985).Google Scholar
- 16.A. Kazakov, in: Dynamics, Bifurcations and Chaos 2015 (DBC II): Extended Abstract of Int. Conf. and School, Nizhny Novgorod, July 20–24, 2015, p. 21.Google Scholar
- 19.A. O. Kazakov, arXiv:1801.00150 [math.DS] (2017).Google Scholar
- 24.G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow–Leningrad (1946).Google Scholar
- 25.V. V. Vagner, in: Proc. Workshop on Vector and Tensor Analysis, No. 5, 301 (1941).Google Scholar
- 26.V. V. Kozlov, Usp. Mekh., 8, No. 3, 85 (1985).Google Scholar