Wavelet analysis of the standard map - Structure and scaling

Details Wavelet analysis of the standard map - Structure and scaling Wavelet analysis of the standard map - Structure and scaling

May 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..263g&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 1-2, p. 263-272.

Mathematics

1

Chaos, Iterative Solution, Transformations (Mathematics), Gray Scale, Hamiltonian Functions, Maps

Scientific paper

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 parameter k = 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. For k = 10 the chaos fills phase space and no structure is apparent; the wavelet transform reveals statistical fluctuations in the distribution of points.

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