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 and a rigorous analysis of a class of representative models, we show that dynamical invariants such as the topological entropy and the fractal dimension of chaotic saddles obey a universal behavior: they exhibit a devil-staircase characteristic as a function of the system parameter.
Lai
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YC
Department of Physics and Astronomy and Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, USA.
Zyczkowski
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K
Grebogi
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