113 research outputs found
Bihamiltonian Reductions and W_n Algebras
We discuss the geometry of the Marsden-Ratiu reduction theorem for a
bihamiltonian manifold. We consider the case of the manifolds associated with
the Gel'fand-Dickey theory, i.e., loop algebras over sl(n+1). We provide an
explicit identification, tailored on the MR reduction, of the
Adler-Gel'fand-Dickey brackets with the Poisson brackets on the MR-reduced
bihamiltonian manifold N. Such an identification relies on a suitable immersion
of the space of sections of the cotangent bundle of N into the algebra of
pseudo differential operators connected to geometrical features of the theory
of (classical) W_n algebras.Comment: LaTeX2e, 23 pages, to be published in J. Geom. Phy
A Note on Fractional KdV Hierarchies
We introduce a hierarchy of mutually commuting dynamical systems on a finite
number of Laurent series. This hierarchy can be seen as a prolongation of the
KP hierarchy, or a ``reduction'' in which the space coordinate is identified
with an arbitrarily chosen time of a bigger dynamical system. Fractional KdV
hierarchies are gotten by means of further reductions, obtained by constraining
the Laurent series. The case of sl(3)^2 and its bihamiltonian structure are
discussed in detail.Comment: Final version to appear in J. Math. Phys. Some changes in the order
of presentation, with more emphasis on the geometrical picture. One figure
added (using epsf.sty). 30 pages, Late
Cantori and dynamical localization in the Bunimovich Stadium
Classical and quantum properties of the Bunimovich stadium in the diffusive
regime are reviewed. In particular, the quantum properties are directly
investigated using an approximate quantum map. Different localized regimes are
found, namely, perturbative, quasi-integrable (due to classical Cantori),
dynamical and ergodic.Comment: RevTeX, 8 pages, to be published in Physica
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