Chaos near a reversible homoclinic bifocus

We show that any neighbourhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on N-symbols for all N≥2. This will be achieved by showing switching associated with networks of secondary homoclinic orbits. We also prove the existence of super-homoclinic orbits (trajectories homoclinic to a network of homoclinic orbits), whose presence leads to a particularly rich structure.