Entropy and bifurcations in a chaotic laser

We compute bounds on the topological entropy associated with a transition to chaos via a boundary crisis of the Poincare return map to a fixed plane of a semiconductor laser with optical injection. Even though this Poincare map is not defined globally in the whole of the plane, we are still able to compute the stable and unstable manifolds of periodic points globally. In this way, we identify a boundary crisis, which involves periodic point with negative eigenvalues, and obtain the information that forms the input of the entropy calculations. The entropy associated with the chaotic attractor is positive at the boundary crisis and persists in a chaotic saddle after the bifurcation.