Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Persistent bundles over a two dimensional compact set   The $C^1$-structurally stable diffeomorphims of a compact manifold are those
that satisfy Axiom A and the strong transversality condition (AS). We
generalize the concept of AS from diffeomorphisms to invariant compact subsets.
Among other properties, we show the structural stability of the AS invariant
compact sets $K$ of surface diffeomorphisms $f$. Moreover if $\hat f$ is the
dynamics of a compact manifold, which fibers over $f$ and such that the bundle
is normally hyperbolic over the non-wandering set of $f_{|K}$, then the bundle
over $K$ is persistent. This provides non trivial examples of persistent
laminations that are not normally hyperbolic.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph