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  • Hénon-Pomeau map  (2)
  • Springer  (2)
  • American Institute of Physics (AIP)
  • 1985-1989  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Computation of the largest Lyapunov exponent by the generalized cell mapping (1986)
    Springer
    Journal of statistical physics 45 (1986), S. 49-61 
    Details
    ISSN: 1572-9613
    Keywords: Strange attractors ; Lyapunov exponents ; cell-to-cell mapping ; generalized cell mapping ; nonlinear dynamical systems ; Hénon-Pomeau map ; forced Duffing system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The method of cell mappings has been developed as an efficient tool for the global study of dynamical systems. One of them, the generalized cell mapping (GCM), describes the behavior of a system in a probabilistic sense, and is essentially a Markov chain analysis of dynamical systems. Since the largest Lyapunov exponent is widely used to characterize attractors of dynamical systems, we propose an algorithm for that quantity by the GCM. This allows us to examine the persistent groups of the GCM in terms of their Lyapunov exponent, thereby connecting them with their counterparts in point mapping systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033076
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Statistics of strange attractors by generalized cell mapping (1985)
    Springer
    Journal of statistical physics 38 (1985), S. 735-761 
    Details
    ISSN: 1572-9613
    Keywords: Strange attractors ; statistical properties of strange attractors ; invariant distribution ; cell-to-cell mapping ; generalized cell mapping ; nonlinear dynamical systems ; Hénon-Pomeau map ; Zaslavskii map ; forced Duffing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010488
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    Paper (German National Licenses)
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