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Junge, O.; Marsden, J.E.; Mezic, I.:
Uncertainty in the Dynamics of Conservative Maps,
Proceedings of the 43rd IEEE CDC, 2004.

This paper studies the effect of uncertainty, using random perturbations, on area preserving maps on the plane. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.

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