Weak Liouville-Arnold Theorems & Their Implications

Details Weak Liouville-Arnold Theorems & Their Implications Weak Liouville-Arnold Theorems & Their Implications

2010-10-31

arxiv.org/abs/1011.0172v3

Mathematics

Dynamical Systems

24 pages, 1 figure; v2 corrects typo in online abstract; v3 includes new title (was: A Weak Liouville-Arnold Theorem), re-arra

Scientific paper

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.

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