Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust and generic properties for piecewise continuous maps on the
  interval   We construct an appropriate metric on the collection of piecewise $\mathcal
C^r$ maps defined on a compact interval. Although this metric space turns out
to be not complete, we show that it is indeed a Baire space. As an application,
we prove the robustness of non-degenerate critical points for this class of
systems and we show the genericity of piecewise Lipschitz maps that admit an
invariant Borel probability measure.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc