Symbolic sequences of one-dimensional quadratic maps points

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

Physica A: Statistical Mechanics and its Applications, 1998, vol. 256, issue 3, 369-382

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.

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Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:256:y:1998:i:3:p:369-382

DOI: 10.1016/S0378-4371(98)00083-1

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