Reversibility, Continued Fractions, and Infinite Meander Permutations of Planar Homoclinic Orbits in Linear Hyperbolic Anosov Maps

Abstract

Meander permutations have been encountered in the context of Gauss words, singularity theory, Sturm global attractors, plane Cartesian billiards, and Temperley–Lieb algebras, among others. In this spirit, we attempt to investigate the difference of orderings of homoclinic orbits on the stable and unstable manifolds of a planar saddle. As an example, we consider reversible linear Anosov maps on the 2-torus, and their relation to continued fraction expansions.