Wavelet Analysis of the Standard Map  Structure and Scaling
Abstract
Wavelet analysis is applied to distributions of points generated by iterating the standard map. The initial condition is chosen so that the points fill the largest chaotic region. When the standard map parameterk=1.3, the distribution of points contains many voids corresponding to islands in the chaotic region. The wavelet transform is dominated by contributions from these islands. Fork=10 the chaos fills phase space and no structure is apparent; the wavelet transform reveals statistical fluctuations in the distribution of points.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 May 1993
 DOI:
 10.1007/BF00699736
 Bibcode:
 1993CeMDA..56..263G
 Keywords:

 Chaos;
 Iterative Solution;
 Transformations (Mathematics);
 Gray Scale;
 Hamiltonian Functions;
 Maps;
 Physics (General);
 Wavelet analysis;
 standard mapping;
 chaotic motion