Rigorous verification of bifurcations of differential equations via the conley index theory

We propose a new approach for capturing bifurcations of (semi)flows by using a topological tool, the Conley index. We can apply this concept to capture bifurcations with rigorous numerics. As an example, we consider the dynamics generated by the Swift-Hohenberg PDE and show that a pitchfork-like bifurcation occurs in a certain region.