Geodesic
Weak Mixing Manifold Homeomorphisms Preserving an Infinite Measure
Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1475-1488

Voir la notice de l'article provenant de la source Cambridge University Press

Let denote the group of all homeomorphisms of a σ-compact manifold which preserve a σ-finite, nonatomic, locally positive and locally finite measure μ. In two recent papers [4, 5] the possible ergodicity of a homeomorphism h in was shown to be related to the homeomorphism h* induced by h on the ends of M. An end of a manifold is, roughly speaking, a distinct way of going to infinity. Those papers demonstrated in particular that always contains an ergodic homeomorphism, paralleling the similar result of Oxtoby and Ulam [11] for compact manifolds with finite measures. Unfortunately the techniques used in [4] and [5] rely on the fact that a skyscraper construction with an ergodic base transformation is ergodic, a result which cannot be extended to finer properties than ergodicity. 
Alpern, Steve; Prasad, Vidhu. Weak Mixing Manifold Homeomorphisms Preserving an Infinite Measure. Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1475-1488. doi: 10.4153/CJM-1987-070-7
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