Applied Mathematics and Mechanics

, Volume 10, Issue 6, pp 553–562 | Cite as

Hope-Landau bifurcations of higher dimensional tori

  • Cheng Chong-qing


The existence of degenerate bifurcations from Tm to Tm+1 is proved under the condition of quasi-periodic critical points.


Mathematical Modeling Industrial Mathematic Dimensional Torus High Dimensional Torus Degenerate Bifurcation 


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  1. [1]
    Ruelle, D. and F. Takens, On the nature of turbulence,Comm. Math. Phys.,20, 23 (1971).CrossRefGoogle Scholar
  2. [2]
    Newhause, S., D. Ruelle and F. Takens, Occurrence of strange axiomA attractors near quasi-periodic flow onT m (m⩾3),Comm. Math. Phys.,64 (1978).Google Scholar
  3. [3]
    Sell, G.R., Bifurcation of higher dimensional tori,Archives for Rational Mechanics and Analysis,69 (1979).Google Scholar
  4. [4]
    Sell, G.R., Resonance and Bifurcation in Hopf-Landau Dynamical System, inNonlinear Dynamics and Turbulence, Pitman, London (1983).Google Scholar
  5. [5]
    Cheng Chong-qing, Hopf-Landau bifurcations of a kind of nonlinear systems, dissertation for doctor degree, Northwestern Polytechnical University, Xi'an, China (1987). (in Chinese)Google Scholar
  6. [6]
    Lin Zhen-sheng,Almost Periodic Linear System and Integral manifolds, Shanghai Scientific and Technological Literature Publishing House, Shanghai, China (1986). (in Chinese)Google Scholar
  7. [7]
    Qian Min, et al., Invariant cycle (integral manifold) bifurcation of non-autonomous system,Acta Math. Sinica,26 (1983). (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology 1989

Authors and Affiliations

  • Cheng Chong-qing
    • 1
  1. 1.Northwestern Polytechnical UniversityXi'an

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