Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Periodic Points of Symplectomorphisms on Surfaces   We construct a symplectic flow on a surface of genus g greater than one with
exactly 2g-2 hyperbolic fixed points and no other periodic orbits. Moreover, we
prove that a (strongly non-degenerate) symplectomorphism of a surface (with
genus g greater than one) isotopic to the identity has infinitely many periodic
points if there exists a fixed point with non-zero mean index. From this
result, we obtain two corollaries, namely that such a symplectomorphism with an
elliptic fixed point or with strictly more than 2g-2 fixed points has
infinitely many periodic points provided that the flux of the isotopy is
"irrational".

6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat