Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded and unbounded behavior for area-preserving rational
  pseudo-rotations   A rational pseudo-rotation $f$ of the torus is a homeomorphism homotopic to
the identity with a rotation set consisting of a single vector $v$ of rational
coordinates. We give a classification for rational pseudo-rotations with an
invariant measure of full support, in terms of the deviations from the constant
rotation $x\mapsto x+v$ in the universal covering. For the simpler case that
$v=(0,0)$, it states that either every orbit by the lifted dynamics is bounded,
or the displacement in some rational direction is uniformly bounded (implying
that the dynamics is annular) or the set of fixed points of $f$ contains a
large continuum which is the complement of a disjoint union of disks (i.e. a
fully essential continuum). In the analytic setting, the latter case is ruled
out. In order to prove this classification, we introduce tools that are of
independent interest and can be applied in a more general setting: in
particular, a geometric result about the quasi-convexity and existence of
asymptotic directions for certain chains of disks, and a Poincar\'e recurrence
theorem on the universal covering for irrotational measures.

17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th