We prove a number of results on the interrelation between the Lpmetric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily Lp-far from the subset A, answering a variant of a question of Polterovich for the Lp-metric.
All Science Journal Classification (ASJC) codes
- !!General Mathematics