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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.

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
Full Text: DOI
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