Evolution of Chaos and Power Spectra in One-Dimensional Maps
Low-dimensional maps have turned out to be useful for discovering and understanding new properties of dynamical systems. Outstanding examples are the Bernoulli shifts  and the β transformations  in ergodic theory and the Lorenz map  and the quadratic model for the onset of fluid turbulence . 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  and a dynamic scaling law near a chaotic transition point [4,6].
KeywordsPower Spectrum Periodic Orbit Lyapunov Exponent Topological Entropy Chaotic Orbit
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