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Suppression of dynamic chaos in Hamiltonian systems

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Abstract

The paper describes the results of a recent numerical study on the canonical mapping with a sawtooth force. The dynamic effects of the formation of invariant resonance structures of various orders, whose presence prevents the development of global chaos and restricts momentum diffusion in the phase space, are discussed. The dynamic situation near an integer resonance separatrix in the neighborhood of the critical state is studied, and the conditions responsible for the stability of this separatrix in the critical state are determined. Along with the mapping, the related continuous Hamiltonian system is considered. For this system, the separatrix mapping and the Mel’nikov-Arnold integral are introduced, whose analysis facilitates understanding the reasons responsible for the unusual dynamics. This dynamics is shown to be preserved under substantial saw shape changes. Relevant new problems and open questions are formulated.

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Authors and Affiliations

  1. Budker Institute of Nuclear Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 11, Novosibirsk, 630090, Russia

    V. V. Vecheslavov

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  1. V. V. Vecheslavov
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Correspondence to V. V. Vecheslavov.

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__________

Translated from Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, Vol. 119, No. 4, 2001, pp. 853–861.

Original Russian Text Copyright © 2001 by Vecheslavov.

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Vecheslavov, V.V. Suppression of dynamic chaos in Hamiltonian systems. J Exp Theor Phys 92, 744–751 (2001). https://doi.org/10.1134/1.1371354

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