Abstract
We consider the motion of a test particle in a compound central potential field on a two-dimensional torus. We discuss three different classes of potentials (attracting, repelling, and mixed) that lead to Hamiltonian systems which have positive Lyapunov exponent almost everywhere and are ergodic. Included among the mixed potentials are smooth potentials without singularities.
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Communicated by Ya. G. Sinai
Partially supported by NSF grant DMS 8806067
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Donnay, V., Liverani, C. Potentials on the two-torus for which the Hamiltonian flow is ergodic. Commun.Math. Phys. 135, 267–302 (1991). https://doi.org/10.1007/BF02098044
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DOI: https://doi.org/10.1007/BF02098044