Max-Planck-Institut für                                                                                       Dresden, Juni 2000
Physik komplexer Systeme, Dresden

Fachrichtung Mathematik,
Institut für Analysis, TU Dresden

DFG-SPP: DYNAMIK (DANSE)

Im Seminar

Dynamische Systeme

dienstags, 15.00-16.30 Uhr,
Seminarraum 3 des Max-Planck-Instituts für Physik komplexer Systeme (MPIPKS),
Nöthnitzerstr. 38, 01187 Dresden

findet am

20.6.2000

der folgende Vortrag statt:

Dr.  Stefan Siegmund, Universität Augsburg
 "Spectral Theory for Nonautonomous Differential Equations"

Alle Interessenten sind herzlich eingeladen.


Abstract : For nonautonomous linear differential equations dx/dt = A(t)x with locally integrable A : R -> R^(N × N) the so-called dichotomy spectrum is introduced. As the closely related Sacker-Sell spectrum for skew-product flows this new spectrum consists of at most N closed intervals, which in contrast to the Sacker-Sell spectrum may be unbounded. In the constant coefficients case these intervals reduce to the real parts of the eigenvalues of A. In any case the spectral intervals are associated with spectral manifolds (vector bundles over R comprising solutions with a common exponential growth rate. The main result is a spectral theorem which describes all possible forms of the dichotomy spectrum.

gez.:


 PD Dr. H. Kantz, MPIPKS Dresden                                              PD Dr. V. Reitmann, TU Dresden