A Note on Integrable Mechanical Systems on Surfaces
Dynamical Systems
2013-10-14 v2 Exactly Solvable and Integrable Systems
Abstract
Let S be a compact, connected surface and H in C^2(T^* S) a Tonelli Hamiltonian. This note extends V. V. Kozlov's result on the Euler characteristic of S when H is real-analytically integrable, using a definition of topologically-tame integrability called semisimplicity. Theorem: If H is 2-semisimple, then S has non-negative Euler characteristic; if H is 1-semisimple and reversible, then S has positive Euler characteristic.
Cite
@article{arxiv.1208.1460,
title = {A Note on Integrable Mechanical Systems on Surfaces},
author = {Leo T. Butler},
journal= {arXiv preprint arXiv:1208.1460},
year = {2013}
}
Comments
7 pages, 1 figure; removed reversibility hypothesis and renamed in v2; to appear in DCDS-A