Evolution of Chaos and Power Spectra in One-Dimensional Maps

  • Hazime Mori
Part of the Springer Series in Synergetics book series (SSSYN, volume 12)


Low-dimensional maps have turned out to be useful for discovering and understanding new properties of dynamical systems. Outstanding examples are the Bernoulli shifts [1] and the β transformations [2] in ergodic theory and the Lorenz map [3] and the quadratic model for the onset of fluid turbulence [4]. In fact these discrete processes have led us not only to a deeper understanding of chaotic orbits in terms of the topological entropy and the Lyapunov exponent, but also to the discovery of a band-splitting transition [5] and a dynamic scaling law near a chaotic transition point [4,6].


Power Spectrum Periodic Orbit Lyapunov Exponent Topological Entropy Chaotic Orbit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Hazime Mori
    • 1
  1. 1.Department of PhysicsKyushu University 33Fukuoka 812Japan

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