Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Smooth Bifurcations of Uniformly Hyperbolic Invariant Manifolds in
  Skew Product Systems: Rigorous Results   In this paper we study the anti-integrable limit scenario of skew-product
systems. We consider a generalization of such systems based on the
Frenkel-Kontorova model, and prove the existence of orbits with any fibered
rotation number in systems of both one and two degrees of freedom. In
particular, our results also apply to two dimensional maps with degenerate
potentials (vanishing second derivative), so extending the results of existence
of Cantori for more general twist maps.
  We also prove that under certain mild regularity conditions on the potential
the structure of the orbits is of Cantor type. From our results we deduce the
existence of the non-smooth folding bifurcation (conjectured by Figueras-Haro,
\textit{Different scenarios for hyperbolicity breakdown in quasiperiodic area
preserving twist maps}, Chaos:25 (2015)).
  Lastly we present a pair of results which are useful in determining if a
potential satisfies the regularity conditions required for the Cantor sets of
orbits to exist and are also of independent interest.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org