Application of fragmentation norms to transported points by Hamiltonian isotopies

概要

We prove that a certain $C^0$-robust condition of a Hamiltonian function $H$ induces the existence of a point transported $\varepsilon$ out of the original point by the Hamiltonian diffeomorphism $\varphi_H$. Related to our observation, we provide a problem on Hamiltonian pseudo-rotations.