A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization

Autor:	Buhovsky, Lev, Feuerstein, Ben, Polterovich, Leonid, Shelukhin, Egor
Rok vydání:	2024
Předmět:	Mathematics - Symplectic Geometry Mathematics - Dynamical Systems 53Dxx (Primary) 58D05 22E65 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Essentially, we prove that every autonomous Hamiltonian diffeomorphism is conjugate to an element C-close in the Hofer metric to one generated by a function of the height. Comment: 30 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.08854 Zobrazit plný text záznamu View this record from Arxiv