Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-hyperbolic ergodic measures and horseshoes in partially hyperbolic
  homoclinic classes   We study a rich family of robustly non-hyperbolic transitive diffeomorphisms
and we show that each ergodic measure is approached by hyperbolic sets in
weak$*$-topology and in entropy. For hyperbolic ergodic measures, it is a
classical result of A. Katok. The novelty here is to deal with non-hyperbolic
ergodic measures.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio