Hans-Otto Walther
Universität Giessen
Colloque
28 septembre 2018 de 16 h 00 à 17 h 00 (heure de Montréal/HNE) Sur place
A delay differential equation with a solution whose shortened segments are dense
Colloque par Hans-Otto Walther (Universität Giessen)
Simple-looking autonomous delay differential equations 
with a real function 
and single time lag 
can generate complicated (chaotic) solution behaviour, depending on the shape of . The same could be shown for equations with a variable, state-dependent delay 
, even for the linear case 
with 
. Here the argument 
of the {\it delay functional} 
is the history of the solution 
between 
and t defined as the function 
given by 
. So the delay alone may be responsible for complicated solution behaviour. In both cases the complicated behaviour which could be established occurs in a thin dust-like invariant subset of the infinite-dimensional Banach space or manifold of functions 
on which the delay equation defines a nice semiflow. The lecture presents a result which grew out of an attempt to obtain complicated motion on a larger set with non-empty interior, as certain numerical experiments seem to suggest. For some 
we construct a delay functional 
, 
an infinite-dimensional subset of the space 
, so that the equation 
has a solution whose {\it short segments} 
, 
, are dense in the space 
. This implies a new kind of complicated behaviour of the flowline 
. Reference: H. O. Walther, {\em A delay differential equation with a solution whose shortened segments are dense}.\\ J. Dynamics Dif. Eqs., to appear.
Adresse
McGill University, Burnside Hall, salle 1104, 805 rue Sherbrooke O