Computer assisted method for proving existence of periodic orbits

Abstract

We introduce a method based on the Conley index theory for proving the existence of a periodic trajectory in a smooth dynamical system in $\mathbb R^n$ where an attracting periodic orbit is numerically observed. We apply this method to prove the existence of a periodic orbit in the Rössler equations, as announced in [Computer assisted proof of the existence of a periodic orbit in the Rössler equations].