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 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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References
Améodo, A., Grasseau, G. & Holschneider, M.: 1988, “Wavelet transform of multifractals,” Phys. Rev. Lett., 61 2281–2284.
Bendjoya, Ph., Slezak, E. and Froeschlé, Cl.: 1991, “The wavelet transform: a new tool for asteroid family determination”, Astron. Astrophys, 251 312–330.
Lichtenberg, A.J. & Lieberman, M.A.: 1983, “Regular and Stochastic Motion,” Applied Mathematical Sciences Vol. 38, Springer-Verlag.
Slezak, E., Bijaoui, A. & Mars, G.: 1990, “ Identification of structures from galaxy counts: use of the wavelet transform,” Astron. Astrophys., 227 301–316.
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© 1993 Springer Science+Business Media Dordrecht
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Gilbert, A.D., Froeschlé, C., Frisch, U. (1993). Wavelet Analysis of the Standard Map: Structure and Scaling. In: Dvorak, R., Henrard, J. (eds) Qualitative and Quantitative Behaviour of Planetary Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2030-2_22
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DOI: https://doi.org/10.1007/978-94-011-2030-2_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4898-9
Online ISBN: 978-94-011-2030-2
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