December 14, 2017 / by Matthew Kvalheim / In news

### A fun fact about the Euler characteristic

There are many equivalent definitions of the Euler characteristic $\chi(Y)$ of a space $Y$. I recently learned another of these, valid in the case that $Y$ is a compact, orientable, smooth manifold.

February 15, 2015 / by George Council / In news

### Rigorous Enclosures of a Slow Manifold

Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast systems. This paper introduces a rigorous numerical method to compute enclosures of the slow manifold of a slow-fast system with one fast and two slow variables.

February 15, 2015 / by George Council / In news

### Bifurcation and chaos in the simple passive dynamic walking model with upper body

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations.