Quelques résultats sur les systèmes dynamiques gaussiens réels

Abstract : The first chapter of this thesis proves that the entropy of a gaussian dynamical system is zero or infinite, according as its spectral measure is singular or not with respect to the Lebesgue measure. This result is extended to the case of a multidimensional action. In the second chapter, we develop a new model for gaussian systems, which are viewed as a transformation of the plane brownian path. This transformation can be inserted in a flow, for which we calculate a mean motion. This model is used in the third chapter to construct two gaussian systems of zero entropy which are not Kakutani-equivalent: one of them is not loosely Bernoulli, whereas the other one (a gaussian-Kronecker system) is loosely Bernoulli. For this, we also need to show a property of the plane brownian motion: the whole path can be recovered knowing only some angles formed by the trajectory.
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  • HAL Id : tel-01546012, version 1

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Thierry de la Rue. Quelques résultats sur les systèmes dynamiques gaussiens réels. Probabilités [math.PR]. Université de Rouen, France, 1994. Français. ⟨tel-01546012⟩

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