Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles
نویسنده
چکیده
For many classes of symplectic manifolds, the Hamiltonian flow of a function with sufficiently large variation must have a fast periodic orbit. This principle is the base of the notion of Hofer-Zehnder capacity and some other symplectic invariants and leads to numerous results concerning existence of periodic orbits of Hamiltonian flows. Along these lines, we show that given a negatively curved manifold M , a neigbourhood UR of M in T ∗M , a sufficiently C-small magnetic field σ and a non-trivial free homotopy class of loops α, then the magnetic flow of certain Hamiltonians supported in UR with big enough minimum, has a one-periodic orbit in α. As a consequence, we obtain estimates for the relative Hofer-Zehnder capacity and the Biran-Polterovich-Salamon capacity of a neighbourhood of M .
منابع مشابه
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