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Wavelet Analysis of the Standard Map: Structure and Scaling

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Qualitative and Quantitative Behaviour of Planetary Systems

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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

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Author information

Authors and Affiliations

  1. Observatoire de Nice, B.P.229, 06304, Nice Cedex 4, France

    A. D. Gilbert, C. Froeschlé & U. Frisch

  2. D.A.M.T.P., Silver St., Cambridge, CB3 9EW, UK

    A. D. Gilbert

Authors
  1. A. D. Gilbert
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  2. C. Froeschlé
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  3. U. Frisch
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Editor information

Editors and Affiliations

  1. Institut für Astronomie, Universitätssternwarte, Vienna, Austria

    R. Dvorak

  2. Département de Mathématique, FNDP, Namur, Belgium

    J. Henrard

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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

  • eBook Packages: Springer Book Archive

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