Chaotic motion in delay equations

Date

Jan 7, 2016

Time

3:15 PM - 4:15 PM

Speaker

Prof. Dr. Bernhard Lani-Wayda

Affiliation

Justus-Liebig-Universität Gießen, Mathematisches Institut

Series

TUD Mathematik Oberseminar Analysis

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. S. Siegmund

Description

Homoclinic orbits are known to cause complicated dynamics since Poincaré, and classical analytical results in this direction were proved by Smale and Shilnikov. Usually a symbolic dynamics description is used to express in which precise sense there exists “chaotic” motion. In delay equations, such as $x'(t) = - \mu x(t) + f(x(t-1))$, apparently chaotic behavior was frequently observed in numerical simulations since the 1970s. Analytical proofs are, generally speaking, still out of reach, but exist for some examples. The talk presents some of these examples and the relevant geometric-topological structures, along with open problems.

Links

• Oberseminar Analysis

Last modified: Oct 15, 2015, 5:11:20 PM