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There are few examples in dynamical systems theory which lend themselves to exact computations of macroscopic variables of interest. One such variable is the Lyapunov exponent which measures the average attraction of an invariant set. This article presents .a family of noninvertible transformations of the plane for which such computations are possible. This model sheds additional insight into the notion of what it can mean for an attracting invariant set to have a riddled basin of attraction.


This article originally appeared in Physical Review Letters (ISSN 0031-9007, ESSN 1079-7114), and is posted in accordance with the Institutional Repository guidelines set by APS. The publisher copy is available online at:



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Billings, L., Curry, J. H., & Phipps, E. (1997). Lyapunov exponents, singularities, and a riddling bifurcation. Physical Review Letters, 79(6), 1018.

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