3 citations · 6 across the 4 of their papers we have counts for
7 papers · 1 filter
Quasi-states and symplectic intersections
Michael Entov, Leonid Polterovich
We establish a link between symplectic topology and a recently emerged branch of functional analysis called the theory of quasi-states and quasi-measures. In the symplectic context…
Calabi quasimorphisms for the symplectic ball
Paul Biran, Michael Entov, Leonid Polterovich
We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms.…
Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory
Gabriel P. Paternain, Leonid Polterovich, Karl Friedrich Siburg
We consider Lagrangian submanifolds lying on a fiberwise strictly convex hypersurface in some cotangent bundle or, respectively, in the domain bounded by such a hypersurface. We es…
Calabi quasimorphism and quantum homology
Michael Entov, Leonid Polterovich
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value…
Propagation in Hamiltonian dynamics and relative symplectic homology
Paul Biran, Leonid Polterovich, Dietmar Salamon
The main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent Hamiltonian systems on the unit cotangent bundle of the torus or of…
An obstruction to conservation of volume in contact dynamics
Leonid Polterovich
A theorem of Moser guarantees that every diffeomorphism of a closed manifold can be isotoped to a volume preserving one. We show that this statement cannot be extended into contact…