Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffeomorphisms with Liao-Pesin set   In this paper we mainly deal with an invariant (ergodic) hyperbolic measure
$\mu$ for a diffeomorphism $f,$ assuming that $f$ is just $C^1$ and for $\mu$
a.e. $x$, the sum of Oseledec spaces corresponding to negative Lyapunov
exponents (quasi-limit-)dominates the sum of Oseledec spaces corresponding to
positive Lyapunov exponents at $x$. We generalize a certain of results of Pesin
theory from $C^{1+\alpha}$ to the $C^1$ system $ (f,\mu)$, including a
sufficient condition for existence of horseshoe, Livshitz theorem, exponential
growth of periodic points, distribution of periodic points, periodic measures,
horseshoes, nonuniform specification and lower semi-continuity of entropy
function etc. In particular, they are applied for $C^1$ partially hyperbolic
systems whose central bundle displays some non-uniform hyperbolicity, including
some robust systems. Moreover, for some $C^1$ partially hyperbolic (not
necessarily volume-preserving) systems, we get some information of Lebesgue
measure on Average-nonuniform hyperbolicityand volume-non-expanding.
  A constructed machinery is developed for $C^1$ (not necessarily
$C^{1+\alpha}$) diffeomorphisms: new Pesin blocks is established topologically
(independent on measures) such that every block has stable manifold theorem and
simultaneously has exponential shadowing. The new construction, different with
classical $C^{1+\alpha}$ ones, is mainly inspired from Liao's
quasi-hyperbolicity and so here we call new blocks by Liao-Pesin blocks and
call the new established $C^1$ Pesin theory by $C^1$ Liao-Pesin Theory.
Liao-Pesin set not only exists for invariant measures, but also exists for
general probability measures, for example, Lebesgue measure (not assuming
invariant) in some partially hyperbolic systems.

1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org