Hamiltonian displacement of bidisks inside cylinders

where the infimum is taken over all compactly supported (Hamiltonian) functions H : R × [0, 1] → R, and writing Ht(x) = H(x, t) the Hofer norm ‖H‖ = ∫ 1 0 supx Ht(x) − infxHt(x)dt. The diffeomorphism φH is the Hamiltonian diffeomorphism generated by H , that is, the time-1 flow of the timedependent vectorfield Xt defined by Xt⌋ω = dHt. The form ω = ∑n i=1 dxi ∧ dyi is the standard symplectic form on R 2n in coordinates x1, y1, ..., xn, yn. It is sometimes convenient to write ‖φ‖ = inf ‖H‖ where the infimum is taken over all Hamiltonian functions H satisfying φH = φ. The notion of displacement energy extends to arbitrary symplectic manifolds, in particular to subsets M ⊂ R. In this case the displacement energy is defined by e(U) = inf{‖H‖|φH(U) ∩ U = ∅}