Universal behavior in the parametric evolution of chaotic saddles

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. As a system parameter changes, chaotic saddles can evolve via an infinite number of homoclinic or heteroclinic tangencies of their stable and unstable manifolds. Based on previous numerical evidence a nd a rigorous analysis of a class of representative models, we show that dy namical invariants such as the topological entropy and the fractal dimensio n of chaotic saddles obey a universal behavior: they exhibit a devil-stairc ase characteristic as a function of the system parameter. [S1063-651X(99)01 605-0].