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Symbolic sequences of one-dimensional quadratic maps points

Author

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  • Pastor, G.
  • Romera, M.
  • Sanz-Martı́n, J.C.
  • Montoya, F.

Abstract

In previous works we introduced the symbolic sequence of the orbit of a Misiurewicz point of a one-dimensional quadratic map and formulae to calculate the symbolic sequences of the orbits of the tip and the cusp points in the Mandelbrot set antenna (an L-map). In this work we generalize these expressions to any map type, and we present simple formulae to directly calculate the symbolic sequences of chaotic bands merging points, pitchfork bifurcation points and stable periodic points in one-dimensional quadratic maps. To conclude, some considerations about the notation of the accumulation points are accomplished.

Suggested Citation

  • Pastor, G. & Romera, M. & Sanz-Martı́n, J.C. & Montoya, F., 1998. "Symbolic sequences of one-dimensional quadratic maps points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 369-382.
    • Handle: RePEc:eee:phsmap:v:256:y:1998:i:3:p:369-382
    DOI: 10.1016/S0378-4371(98)00083-1
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