1,012 research outputs found
The Weierstrass representation of closed surfaces in
In the present paper which a sequel to dg-ga/9511005 and dg-ga//9610013 a
global Weierstrass representation of an arbitrary closed oriented surface of
genus in the the three-space is constructed. The Weierstrass spectrum
of a torus immersed into is introduced and finite-zone planes as well as
finite-zone solutions to the modified Novikov-Veselov equations are
constructed.Comment: 15 pages, LaTeX; Preprint no. 291, SFB 288, TU-Berli
On the integrability of the n-centre problem
It is known that for centres and positive energies the -centre
problem of celestial mechanics leads to a flow with a strange repellor and
positive topological entropy.
Here we consider the energies above some threshold and show: Whereas for
arbitrary independent integrals of Gevrey class exist, no
real-analytic (that is, Gevrey class 1) independent integral exists.Comment: 22 pages, a short announcement see in math.DS/031242
Trace formula for the magnetic Laplacian
The Guillemin-Uribe trace formula is a semiclassical version of the Selberg
trace formula and more general Duistermaat-Guillemin formula for elliptic
operators on compact manifolds, which reflects the dynamics of magnetic
geodesic flows in terms of eigenvalues of a natural differential operator (the
magnetic Laplacian) associated with the magnetic field. In this paper, we give
a survey of basic notions and results related with the Guillemin-Uribe trace
formula and provide concrete examples of its computation for two-dimensional
constant curvature surfaces with constant magnetic fields and for the Katok
example.Comment: 37 pages, v2: minor corrections, references adde
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