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The universal cardinal ordering of fixed points

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  • San Martín, Jesús
  • Moscoso, Ma José
  • González Gómez, A.

Abstract

We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. Interestingly enough, it is important to point that this theorem needs no previous information about any other orbit; also the cardinal ordering is achieved automatically with no need to compare numerical values associated with every point of the orbit (as would be the case if kneading theory were used).

Suggested Citation

  • San Martín, Jesús & Moscoso, Ma José & González Gómez, A., 2009. "The universal cardinal ordering of fixed points," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1996-2007.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1996-2007
    DOI: 10.1016/j.chaos.2009.03.184
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    References listed on IDEAS

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