37,819 research outputs found
Affine Weyl groups, discrete dynamical systems and Painleve equations
A new class of representations of affine Weyl groups on rational functions
are constructed, in order to formulate discrete dynamical systems associated
with affine root systems. As an application, some examples of difference and
differential systems of Painleve type are discussed.Comment: AMSLaTeX, 16 page
Lie algebroid structures on a class of affine bundles
We introduce the notion of a Lie algebroid structure on an affine bundle
whose base manifold is fibred over the real numbers. It is argued that this is
the framework which one needs for coming to a time-dependent generalization of
the theory of Lagrangian systems on Lie algebroids. An extensive discussion is
given of a way one can think of forms acting on sections of the affine bundle.
It is further shown that the affine Lie algebroid structure gives rise to a
coboundary operator on such forms. The concept of admissible curves and
dynamical systems whose integral curves are admissible, brings an associated
affine bundle into the picture, on which one can define in a natural way a
prolongation of the original affine Lie algebroid structure.Comment: 28 page
Fully oscillating sequences and weighted multiple ergodic limit
We prove that fully oscillating sequences are orthogonal to multiple ergodic
realizations of affine maps of zero entropy on compact abelian groups. It is
more than what Sarnak's conjecture requires for these dynamical systems
- …