118 research outputs found
Remarks on step cocycles over rotations, centralizers and coboundaries
By using a cocycle generated by the step function over an irrational rotation , we present examples which illustrate different aspects
of the general theory of cylinder maps. In particular, we construct non ergodic
cocycles with ergodic compact quotients, cocycles generating an extension
with a small centralizer. The constructions are related
to diophantine properties of
Centralizer and liftable centralizer of special flows over rotations
The liftable centralizer for special flows over irrational rotations is
studied. It is shown that there are such flows under piecewise constant roof
functions which are rigid and whose liftable centralizer is trivial
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Mini-Workshop: Dynamics of Cocycles and One-Dimensional Spectral Theory
Many spectral questions about one-dimensional Schrödinger operators with quasi-periodic potentials can be reduced to dynamical questions about certain quasi-periodic SL(2, R)-valued cocycles. This connection has recently been employed to prove a number of long-standing conjectures. The aim of this mini-workshop was to bring together people from both spectral theory and dynamical systems in order to further develop and exploit the dynamical approach to quasi-periodic Schrödinger operators
Quantization of multidimensional cat maps
In this work we study cat maps with many degrees of freedom. Classical cat
maps are classified using the Cayley parametrization of symplectic matrices and
the closely associated center and chord generating functions. Particular
attention is dedicated to loxodromic behavior, which is a new feature of
two-dimensional maps. The maps are then quantized using a recently developed
Weyl representation on the torus and the general condition on the Floquet
angles is derived for a particular map to be quantizable. The semiclassical
approximation is exact, regardless of the dimensionality or of the nature of
the fixed points.Comment: 33 pages, latex, 6 figures, Submitted to Nonlinearit
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