Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalues of transformations arising from irrational rotations and
  step functions. (Valeurs propres de transformations li\'ees aux rotations
  irrationnelles et aux fonctions en escalier)   Given an irrational rotation $T$ on $\M T$ we settle necessary and sufficient
conditions on a step function $\phi$ and $t\in \M T$ for the existence of
measurable solutions to the cohomogical equation $$\exp{(2i\pi\phi)}=\e{2i\pi
t}f/f\rond T.$$ This yields a characterization of eigenvalues and
eigenfunctions for several transformations arising from irrational rotations
and step functions: cylinder flows, special flows, induced maps... From there
we give constructions of special flows and three-interval exchange
transformations with unusual spectral properties. In both cases we exhibit
examples with Kronecker factors of infinite rank. We also construct
three-interval exchange transformations which are non-trivially conjugate to
irrational rotations or to odometers. Similarly there exist special flows over
irrational rotations which are non-trivially conjugate to translations flows on
$\M T^2$ or on solenoids. Finally, we prove a regularization property which
allows us to give similar examples of special flows with smooth ceiling
functions, under natural Diophantine conditions for the rotation.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: nlin