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math.DG2000
Periodic orbits of Hamiltonian flows near symplectic extrema
Viktor L. Ginzburg, Ely Kerman
For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a conseq…
math.DG2000
Grothendieck Groups of Poisson Vector Bundles
Viktor L. Ginzburg
A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of t…
math.DG2000
The Hamiltonian Seifert Conjecture: Examples and Open Problems
Viktor L. Ginzburg
Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian…