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Misiurewicz point patterns generation in one-dimensional quadratic maps

Author

Listed:
  • Pastor, G.
  • Romera, M.
  • Alvarez, G.
  • Montoya, F.

Abstract

In a family of one-dimensional quadratic maps, Misiurewicz points are unstable and the orbits of such a points are repulsive. On the contrary, the orbits of superstable periodic points are attractive. Here we study the patterns of the symbolic sequences of both Misiurewicz and superstable periodic points, and show that a Misiurewicz point pattern can be obtained as the limit of the sum of a superstable periodic orbit pattern plus itself or some of its heredity transmitters repeated an infinite number of times. Inversely, when a Misiurewicz point pattern is given, we also show that it is possible to find both the superstable periodic orbit pattern and the heredity transmitters that generate such a pattern.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:292:y:2001:i:1:p:207-230
    DOI: 10.1016/S0378-4371(00)00586-0
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    References listed on IDEAS

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    1. Pastor, G. & Romera, M. & Montoya, F., 1996. "On the calculation of Misiurewicz patterns in one-dimensional quadratic maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 536-553.
    2. Romera, M. & Pastor, G. & Montoya, F., 1996. "Misiurewicz points in one-dimensional quadratic maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 517-535.
    3. 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.
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    Cited by:

    1. Pastor, G. & Romera, M. & Álvarez, G. & Arroyo, D. & Montoya, F., 2007. "On periodic and chaotic regions in the Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 15-25.

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