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Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés. (Ergodic properties, in infinite measure, of certain fibered dynamical systems). (French) Zbl 0693.58011

Summary: We study the ergodic properties of a class of dynamical systems with infinite invariant measure. This class contains skew-products of Anosov systems with \({\mathbb{R}}^ d\). The results are applied to the K-property of skew-products and also to the ergodicity of the geodesic flow on abelian coverings of compact manifolds with constant negative curvature.

MSC:

37A99 Ergodic theory
37C10 Dynamics induced by flows and semiflows
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[1] DOI: 10.1070/RM1972v027n04ABEH001383
[2] Spitzer, Principles of random walks (1964) · Zbl 0119.34304
[3] Rudolph, Asymptotically brownian skew products give non loosely Bernoulli · Zbl 0655.58034
[4] Guivarc’h, Théorie du Potentiel pp 301– (1983)
[5] Guivarc’h, Annales de l’Inst. H. Poincaré 24 pp 73– (1988)
[6] Gottschalk, Amer. Math. Soc. 36 pp none– (1955)
[7] Choquet, C.R.A.S. 250 pp 799– (1960)
[8] DOI: 10.1007/BF02046760 · Zbl 0459.60099
[9] DOI: 10.1007/BF01389848 · Zbl 0311.58010
[10] DOI: 10.2307/2373793 · Zbl 0282.58009
[11] Bowen, Equilibrium states and the ergodic theory of Anosov diSeomorphisms (1975) · Zbl 0308.28010
[12] DOI: 10.1007/BF02757718 · Zbl 0307.28014
[13] Rudolph, Z” and R” cocycle extensions and complementary algebras
[14] Rees, Ergod. Th. ? Dynam. Sys. 1 pp 107– (1981)
[15] DOI: 10.1007/BF02757724 · Zbl 0305.28008
[16] DOI: 10.1007/BF00534111
[17] Lifshits, Math. Zametki 10 pp 555– (1971)
[18] Le Page, Theoremes limites pour les produits de matrices aleatoires pp 355– (1982)
[19] DOI: 10.1007/BF01390069 · Zbl 0467.58016
[20] DOI: 10.2307/1971397 · Zbl 0523.28018
[21] Guivarc’h, C.R.A.S. 292 pp 851– (1981)
[22] Guivarc’h, Marches aleatoires sur les groupes de Lie (1977) · Zbl 0367.60081
[23] Varopoulos, C.R.A.S. 302 pp 203– (1986)
[24] Sullivan, I.H.E.S. Publ. Math. 50 pp 171– (1979)
[25] DOI: 10.1090/S0002-9904-1967-11798-1 · Zbl 0202.55202
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