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Stochasticity near resonances in a kind of near-integrable Hamiltonian systems based on smale horseshoes

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Abstract

In this paper, a method is developed to detect the appearance of stochasticity in a kind of near-integrable Hamiltonian system with two time-scales. One is fast and the other slow. The stochasticity is showed to be chaos in the sense of Smale horseshoes actually. A stochastic web is discovered in our example, by use of the results obtained in this paper.

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Authors and Affiliations

  1. Xi'an Institute of Technology, Xi'an

    Dong Guang-mao

  2. Suzhou University, Suzhou

    Liu Zheng-rong

  3. LNM, Institute of Mechanics, Chinese Academy of Sciences, China

    Liu Zheng-rong

  4. Shanghai Maritime University, Shanghai

    Xu Zheng-fan

Authors
  1. Dong Guang-mao
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  2. Liu Zheng-rong
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  3. Xu Zheng-fan
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Additional information

Supported partly by the National Natural Science Foundations of China.

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Guang-mao, D., Zheng-rong, L. & Zheng-fan, X. Stochasticity near resonances in a kind of near-integrable Hamiltonian systems based on smale horseshoes. Appl Math Mech 13, 11–16 (1992). https://doi.org/10.1007/BF02450424

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  • DOI: https://doi.org/10.1007/BF02450424

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