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Potentials on the two-torus for which the Hamiltonian flow is ergodic. (English) Zbl 0719.58022
The authors examine the motion of a point particle in the potential field on a two-dimensional torus of symmetric potentials of finite range. Three different classes of potentials are discussed: attracting, repelling and mixed (including smooth potentials without singularities) that lead to Hamiltonian systems which have positive Lyapunov exponent almost everywhere and are ergodic.
Reviewer: R.Cowen (Gaborone)

37A99 Ergodic theory
37C10 Dynamics induced by flows and semiflows
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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