N. Ananikian, R. Artuso, L. Chakhmakhchyan
We consider the superstable cycles of the Q-state Potts (QSP) and the three-site interaction antiferromagnetic Ising (TSAI) models on recursive lattices. The rational mappings describing the models' statistical properties are obtained via the recurrence relation technique. We provide analytical solutions for the superstable cycles of the second order for both models. A particular attention is devoted to the period three window. Here we present an exact result for the superstable orbit of the third order for the QSP and a numerical solution for the TSAI model. Additionally, we point out a non-trivial connection between bifurcation and superstability: in some regions of parameters a superstable cycle is not followed by a doubling bifurcation. Furthermore, we implement the symbolic dynamics technique for understanding the changes taking place at points of superstability. The method allows us to distinguish areas between two consecutive superstable orbits and detect transitions between them by means of a generic symbolic sequence.
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http://arxiv.org/abs/1307.6038
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