Harry Furstenberg

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0. Summary. The objects of ergodic theory -measure spaces with measure-preserving transformation groups-wil l be called processes, those of topological dynamics-compact metric spaces with groups of homeomorphisms-will be called flows. We shall be concerned with what may be termed the "arithmetic" of these classes of objects. One may form products of(More)
We prove the following theorem of Borel: // G is a semisimple Lie group, H a closed subgroup such that the quotient space G/H carries finite measure, then for any finite-dimensional representation of G, each H-invariant subspace is G-invariant. The proof depends on a consideration of measures on projective spaces. The following is a relatively elementary(More)
Introduction. Poincaré is largely responsible for the transformation of celestial mechanics from the study of individual solutions of differential equations to the global analysis of phase space. A system of differential equations such as those which embody the laws of Newtonian mechanics generates a one-parameter group of transformation of the manifold(More)
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