Given a $n$-dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank $d$, where $n$ and $d$ are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in ...
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Given a $n$-dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank $d$, where $n$ and $d$ are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained. The main ingredients of the author's method are the theory of Brownian motion, the analysis of the heat diffusions on Riemannian manifolds, the ergodic theory in discrete dynamics and a geometric study of laminations.
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Add this copy of Oseledec Multiplicative Ergodic Theorem for Laminations to cart. $50.74, good condition, Sold by ThriftBooks-Atlanta rated 5.0 out of 5 stars, ships from Brownstown, MI, UNITED STATES, published 2017 by American Mathematical Society.
Add this copy of Oseledec Multiplicative Ergodic Theorem for Laminations to cart. $94.60, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2017 by Amer Mathematical Society.
