Generically, Arnold-Liouville Systems Cannot be Bi-Hamiltonian

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2021
• Hauptverfasser: Boualem, Hassan, Brouzet, Robert
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2021
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211431
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Generically, Arnold-Liouville Systems Cannot be Bi-Hamiltonian. Hassan Boualem and Robert Brouzet. SIGMA 17 (2021), 096, 17 pages

We state and prove that a certain class of smooth functions, said to be BH-separable, is a meagre subset for the Fréchet topology. Because these functions are the only admissible Hamiltonians for Arnold-Liouville systems admitting a bi-Hamiltonian structure, we get that, generically, Arnold-Liouvill...