Abstract
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. We develop a technique for constructing explicitly all their periodic orbits as perturbations of Anosov orbits, combining methods of arithmetic and symbolic dynamics. We find that the parameter dependence of periodic orbits is given by rational functions, and compute numerically the population of periodic orbits as a function of the parameter.
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