Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^{r}-$prevalence of stable ergodicity for a class of partially
  hyperbolic systems   We prove that for $r \in \mathbb{N}_{\geq 2} \cup \{\infty\}$, for any
dynamically coherent, center bunched and strongly pinched volume preserving
$C^r$ partially hyperbolic diffeomorphism $f \colon X \to X$, if either (1) its
center foliation is uniformly compact, or (2) its center-stable and
center-unstable foliations are of class $C^1$, then there exists a $C^1$-open
neighbourhood of $f$ in ${\rm Diff}^r(X,\mathrm{Vol})$, in which stable
ergodicity is $C^r$-prevalent in Kolmogorov's sense. In particular, we verify
Pugh-Shub's stable ergodicity conjecture in this region. This also provides the
first result that verifies the prevalence of stable ergodicity in the
measure-theoretical sense. Our theorem applies to a large class of algebraic
systems. As applications, we give affirmative answers in the strongly pinched
region to: 1. an open question of Pugh-Shub in \cite{PS}; 2. a generic version
of an open question of Hirsch-Pugh-Shub in \cite{HPS}; and 3. a generic version
of an open question of Pugh-Shub in \cite{HPS}.

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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci