# Hans-Otto Walther

Universität Giessen

September 28, 2018 from 16:00 to 17:00 (Montreal/Miami time) On location

Colloquium presented by **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.

**Address**