22 research outputs found
Rigid fibers of spinning tops
(Non-)displaceability of fibers of integrable systems has been an important
problem in symplectic geometry. In this paper, for a large class of classical
Liouville integrable systems containing the Lagrangian top, the Kovalevskaya
top and the C. Neumann problem, we find a non-displaceable fiber for each of
them. Moreover, we show that the non-displaceable fiber which we detect is the
unique fiber which is non-displaceable from the zero-section. As a special case
of this result, we also show that a singular level set of a convex Hamiltonian
is non-displaceable from the zero-section. To prove these results, we use the
notion of superheaviness introduced by Entov and Polterovich.Comment: 21 pages; some notations in Section 4 change
Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
The first author introduced a relative symplectic capacity for a
symplectic manifold and its subset which measures the
existence of non-contractible periodic trajectories of Hamiltonian isotopies on
the product of with the annulus . In
the present paper, we give an exact computation of the capacity of the
-torus relative to a Lagrangian submanifold
which implies the existence of non-contractible Hamiltonian
periodic trajectories on . Moreover, we give a lower
bound on the number of such trajectories.Comment: 24 pages, 6 figure
APPLICATION OF FRAGMENTATION NORMS TO TRANSPORTED POINTS BY HAMILTONIAN ISOTOPIES (Geometry, Algebra and Combinatorics in Transformation group theory)
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