Critical exponent for gap filling at crisis

A crisis in chaotic dynamical systems is characterized by the conversion of a nonattracting, Cantor-set-like chaotic saddle into a chaotic attractor. The gaps in between various pieces of the chaotic saddle are densely filled after the crisis. We give a quantitative scaling theory for the growth of the topological entropy for a major class of crises, the interior crisis. The theory is confirmed by numerical experiments.