Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shy shadows of infinite-dimensional partially hyperbolic invariant sets   Let $\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset
of an infinite-dimensional Banach space such that the image of its derivative
$D_F \mathcal{R}$ is dense for every $F$. Let $\Omega$ be a compact, forward
invariant and partially hyperbolic set of $\mathcal{R}$ such that
$\mathcal{R}\colon \Omega\rightarrow \Omega$ is onto. The $\delta$-shadow
$W^s_\delta(\Omega)$ of $\Omega$ is the union of the sets $$W^s_\delta(G)=
\{F\colon dist(\mathcal{R}^iF, \mathcal{R}^iG) \leq \delta, \ for \ every \
i\geq 0 \},$$ where $G \in \Omega$. Suppose that $W^s_\delta(\Omega)$ has
transversal empty interior, that is, for every $C^{1+Lip}$ $n$-dimensional
manifold $M$ transversal to the distribution of dominated directions of
$\Omega$ and sufficiently close to $W^s_\delta(\Omega)$ we have that $M\cap
W^s_\delta(\Omega)$ has empty interior in $M$. Here $n$ is the finite dimension
of the strong unstable direction. We show that if $\delta'$ is small enough
then $$\cup_{i\geq 0}\mathcal{R}^{-i}W^s_{\delta'} (\Omega)$$ intercepts a
$C^k$-generic finite dimensional curve inside the Banach space in a set of
parameters with zero Lebesgue measure, for every $k\geq 0$. This extends to
infinite-dimensional dynamical systems previous studies on the Lebesgue measure
of stable laminations of invariants sets.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat