Positive-Entropy Integrable Systems and the Toda Lattice, II
arXiv:0906.1762 · doi:10.1017/S0305004110000356
Abstract
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.
46 pages, 9 tables, 3 figures. To appear in Math. Proc. Camb. Phi. Soc
References in corpus (7)
- Integrable geodesic flow with positive topological entropy
- Rigidity of measurable structure for Z^d-actions by automorphisms of a torus
- Invariant fibration of geodesic flows
- The Maslov cocycle, smooth structures and real-analytic complete integrability
- Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain
- Positive-Entropy Integrable Systems and the Toda Lattice, II
- The Maslov index and nondegenerate singularities of integrable systems