Geodesic
Integrable Geodesic Flows on the Suspensions of Toric Automorphisms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 46-63

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Integrable geodesic flows are studied on suspensions of toric automorphisms. It is shown that, for linear automorphisms with real spectrum, such flows always exist. Their entropy characteristics are investigated. In particular, in the case of hyperbolic automorphisms, we describe explicitly a closed invariant subset on which the topological entropy of the geodesic flow is positive. 
@article{TM_2000_231_a1,
     author = {A. V. Bolsinov and I. A. Taimanov},
     title = {Integrable {Geodesic} {Flows} on the {Suspensions} of {Toric} {Automorphisms}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {46--63},
     publisher = {mathdoc},
     volume = {231},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2000_231_a1/}
}
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A. V. Bolsinov; I. A. Taimanov. Integrable Geodesic Flows on the Suspensions of Toric Automorphisms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems, automata, and infinite groups, Tome 231 (2000), pp. 46-63. http://geodesic.mathdoc.fr/item/TM_2000_231_a1/