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Richness of chaotic dynamics in nonholonomic models of a Celtic stone. (English) Zbl 1417.37222
Summary: We study the regular and chaotic dynamics of two nonholonomic models of a Celtic stone. We show that in the first model (the so-called BM-model of a Celtic stone) the chaotic dynamics arises sharply, during a subcritical period doubling bifurcation of a stable limit cycle, and undergoes certain stages of development under the change of a parameter including the appearance of spiral (Shilnikov-like) strange attractors and mixed dynamics. For the second model, we prove (numerically) the existence of Lorenz-like attractors (we call them discrete Lorenz attractors) and trace both scenarios of development and break-down of these attractors.

MSC:
37J60 Nonholonomic dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G35 Dynamical aspects of attractors and their bifurcations
70F25 Nonholonomic systems related to the dynamics of a system of particles
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