Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (1): 11-16.

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STOCHASTICITY NEAR RESONANCES IN A KIND OF NEAR-INTEGRABLE HAMILTONIAN SYSTEMS BASED ON SMALE HORSESHOES

Dong Guang-mao1, Liu Zeng-rong2, Xu Zheng-fan3   

  1. 1. Xi’an Institute of Technology, Xi’an;
    2. Suzhou University, Suzhou; LNM, Institute of Mechanics, Chinese Academy of Sciences;
    3. Shanghai Maritime University, Shanghai
  • Received:1991-02-01 Online:1992-01-18 Published:1992-01-18

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.

Key words: stochasticity, Smale horseshoe, Ω -stability, time-scale, stochastic web

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