Wavelet analysis and nonlinear dynamics in a nonextensive setting

We undertake the study of signals originated in time-dependent nonlinear systems by recourse to a wavelet-based multiresolution analysis as adapted to a nonextensive (Tsallis) scenario. Diverse applications are discussed. It is shown that the Tsallis environment provides one with more detailed information than the conventional Shannon one.

[1]  A. Aldroubi,et al.  Wavelets in Medicine and Biology , 1997 .

[2]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[3]  A. R. Plastino,et al.  Information theory, approximate time dependent solutions of Boltzmann's equation and Tsallis' entropy , 1994 .

[4]  Michael F. Shlesinger,et al.  Perspectives in biological dynamics and theoretical medicine. , 1987, Annals of the New York Academy of Sciences.

[5]  A. Babloyantz,et al.  Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle , 1985 .

[6]  Michael Unser,et al.  A family of polynomial spline wavelet transforms , 1993, Signal Process..

[7]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[8]  H. Schuster.  Deterministic chaos: An introduction , 1984 .

[9]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[10]  A. R. Plastino,et al.  Stellar polytropes and Tsallis' entropy , 1993 .

[11]  A. R. Plastino,et al.  Tsallis' entropy, Ehrenfest theorem and information theory , 1993 .

[12]  R. Quiroga,et al.  Chaos in Brain Function , 1990 .

[13]  C. Chui.  Wavelet Analysis and Its Applications , 1992 .

[14]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[15]  Boghosian.  Thermodynamic description of the relaxation of two-dimensional turbulence using Tsallis statistics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.