3 citations · 6 across the 4 of their papers we have counts for
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math.DG1999
On the asymptotic geometry of area-preserving maps
Leonid Polterovich, Karl Friedrich Siburg
We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that…
math.DG1998
Hamiltonian loops from the ergodic point of view
Leonid Polterovich
The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transforma…
math.DG1998
Hofer's diameter and Lagrangian intersections
Leonid Polterovich
We prove that the group of Hamiltonian diffeomorphisms of the 2-sphere has infinite diameter with respect to Hofer's metric. Our approach is based on the theory of Lagrangian inter…