Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodic optimization of prevalent super-continuous functions   Given a dynamical system, we say that a performance function has property P
if its time averages along orbits are maximized at a periodic orbit. It is
conjectured by several authors that for sufficiently hyperbolic dynamical
systems, property P should be typical among sufficiently regular performance
functions. In this paper we address this problem using a probabilistic notion
of typicality that is suitable to infinite dimension: the concept of prevalence
as introduced by Hunt, Sauer, and Yorke. For the one-sided shift on two
symbols, we prove that property P is prevalent in spaces of functions with a
strong modulus of regularity. Our proof uses Haar wavelets to approximate the
ergodic optimization problem by a finite-dimensional one, which can be
conveniently restated as a maximum cycle mean problem on a de Bruijin graph.

10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas