Details

Autor(en) / Beteiligte

• Butler, Leo T.
• Sorrentino, Alfonso

Titel

Weak Liouville-Arnol′d Theorems and Their Implications

Ist Teil von

• Communications in mathematical physics, 2012-10, Vol.315 (1), p.109-133

Ort / Verlag

Berlin/Heidelberg: Springer-Verlag

Erscheinungsjahr

2012

Link zum Volltext

Quelle

SpringerLink Journals

Beschreibungen/Notizen

• 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-Arnol′d 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.