Positive-Entropy Integrable Systems and the Toda Lattice, II

Details Positive-Entropy Integrable Systems and the Toda Lattice, II Positive-Entropy Integrable Systems and the Toda Lattice, II

2009-06-09

arxiv.org/abs/0906.1762v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

46 pages, 9 tables, 3 figures. To appear in Math. Proc. Camb. Phi. Soc

Scientific paper

This note constructs completely integrable convex Hamiltonians on the cotangent bundle of certain k-dimensional torus bundles over an l-dimensional torus. A central role is played by the Lax representation of a Bogoyavlenskij-Toda lattice. The classification of these systems, up to iso-energetic topological conjugacy, is related to the classification of abelian groups of Anosov toral automorphisms by their topological entropy function.

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