Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbations of geodesic flows by recurrent dynamics   We consider a geodesic flow on a compact manifold endowed with a Riemannian
(or Finsler, or Lorentz) metric satisfying some generic, explicit conditions.
We couple the geodesic flow with a time-dependent potential, driven by an
external flow on some other compact manifold. If the external flow satisfies
some very general recurrence condition, and the potential satisfies some
explicit conditions that are also very general, we show that the coupled system
has orbits whose energy grows at a linear rate with respect to time. This
growth rate is optimal. We also show the existence of symbolic dynamics. The
existence of orbits whose energy grows unboundedly in time is related to
Arnold's diffusion problem. A particular case of this phenomenon is obtained
when the external dynamical system is quasi-periodic, of rationally independent
frequency vector, not necessarily Diophantine, thus extending earlier results.
We also recover `Mather's acceleration theorem' for time-periodic
perturbations. Since the general class of perturbations that we consider in
this paper are not characterized by a frequency of motion, we are not able to
use KAM or Aubry-Mather or averaging theory. We devise a new mechanism to
construct orbits whose energy evolves in a prescribed fashion. This mechanism
intertwines the inner dynamics restricted to some normally hyperbolic manifold
with the outer dynamics corresponding to two distinct choices of homoclinic
excursions to that manifold. As this mechanism uses very coarse information on
the dynamics, it is potentially of wider applicability.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys