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Windows in one-dimensional maps

Author

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  • Post, Thijs
  • Capel, Hans W.

Abstract

The window structure in the chaotic part of the parameter space of one-dimensional maps is described in detail. Explicit expressions are derived for both the internal structure and the width of the periodic windows, by considering a universal local submap. Both features are found to depend only on the order of the extremum of this submap. Moreover, the windows can be ordered in trees. The various branches of these trees define (accumulating) families of windows, for which exact scaling relations can be derived. Finally, we discuss an extension of our description of window phenomena into two dimensions.

Suggested Citation

  • Post, Thijs & Capel, Hans W., 1991. "Windows in one-dimensional maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 62-100.
    • Handle: RePEc:eee:phsmap:v:178:y:1991:i:1:p:62-100
    DOI: 10.1016/0378-4371(91)90075-N
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    References listed on IDEAS

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    1. Post, T. & Capel, H.W. & Van der Weele, J.P., 1989. "Phase-length distributions in intermittent band switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 321-350.
    2. Levy, Joaquim Vieira Ferreira & Werlang, Sérgio Ribeiro da Costa, 1988. "Congelamento com abono salarial gerando excesso de demanda," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 134, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. Van Der Weele, J.P. & Capel, H.W. & Kluiving, R., 1987. "Period doubling in maps with a maximum of order z," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 145(3), pages 425-460.
    4. Skogan, Wesley G., 1982. "Police and Community in Japan. By Walter L. Ames. (Berkeley: University of California Press, 1981. Pp. xvi + 245. $22.50.)," American Political Science Review, Cambridge University Press, vol. 76(3), pages 679-680, September.
    5. Van der Weele, J.P. & Capel, H.W. & Valkering, T.P. & Post, T., 1988. "The squeeze effect in non-integrable Hamiltonian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(3), pages 499-532.
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    Cited by:

    1. Pastor, G. & Romera, M. & Alvarez, G. & Montoya, F., 2001. "Misiurewicz point patterns generation in one-dimensional quadratic maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 207-230.
    2. San Martín, Jesús & Rodríguez-Pérez, Daniel, 2009. "Conjugation of cascades," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 666-681.

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