Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic Fixed Points and Periodic Orbits of Hamiltonian
  Diffeomorphisms   We prove that for a certain class of closed monotone symplectic manifolds any
Hamiltonian diffeomorphism with a hyperbolic fixed point must necessarily have
infinitely many periodic orbits. Among the manifolds in this class are complex
projective spaces, some Grassmannians, and also certain product manifolds such
as the product of a projective space with a symplectically aspherical manifold
of low dimension.
  A key to the proof of this theorem is the fact that the energy required for a
Floer connecting trajectory to approach an iterated hyperbolic orbit and cross
its fixed neighborhood is bounded away from zero by a constant independent of
the order of iteration. This result, combined with certain properties of the
quantum product specific to the above class of manifolds, implies the existence
of infinitely many periodic orbits.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th