Weak Liouville-Arnold Theorems & Their Implications
Abstract
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnold theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians.
Cite
@article{arxiv.1011.0172,
title = {Weak Liouville-Arnold Theorems & Their Implications},
author = {Leo T. Butler and Alfonso Sorrentino},
journal= {arXiv preprint arXiv:1011.0172},
year = {2012}
}
Comments
24 pages, 1 figure; v2 corrects typo in online abstract; v3 includes new title (was: A Weak Liouville-Arnold Theorem), re-arrangement of introduction, re-numbering of main theorems; v4 updates the authors' email and physical addresses, clarifies notation in section 4. Final version