Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometrical proof of the persistence of normally hyperbolic
  submanifolds   We present a simple, computation free and geometrical proof of the following
classical result: for a diffeomorphism of a manifold, any compact submanifold
which is invariant and normally hyperbolic persists under small perturbations
of the diffeomorphism. The persistence of a Lipschitz invariant submanifold
follows from an application of the Schauder fixed point theorem to a graph
transform, while smoothness and uniqueness of the invariant submanifold are
obtained through geometrical arguments. Moreover, our proof provides a new
result on persistence and regularity of "topologically" normally hyperbolic
submanifolds, but without any uniqueness statement.

25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph