Periodic orbits of the sawtooth maps
The sawtooth maps are a one-parameter family of chaotic area-preserving maps of the 2-torus, which become Anosov systems for special values of the parameter. The purpose of this paper is to carry out a systematic study of the periodic orbits of the sawtooth maps, based on the knowledge of Anosov orbits. Since the sawtooth maps are piecewise linear, the authors of this paper are able to construct the parameter dependence of the sawtooth orbits (perturbed Anosov orbits) explicitly in terms of rational functions with integer coefficients. The essential ingredients for this method are arithmetic and symbolic dynamics. Arithmetical methods are used to compute the unperturbed (i.e., Anosov) orbits, which are then coded as symbol sequences. The latter are then used to classify periodic orbits and to construct explicitly their parameter dependence.
scientific article; zbMATH DE number 4058481