Oseledec multiplicative ergodic theorem for laminations
"Given a -dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank where and 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, we define the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. We also prove an Oseledec multiplicative ergodic theorem in thi…
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- Full title :Oseledec multiplicative ergodic theorem for laminations / Viêt-Anh Nguyên.
Summary
"Given a -dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank where and 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, we define the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. We also prove 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 we establish 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 our 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."--Publisher website
Read More ↓Edition Statements
- Publication Date:©2016
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2016
Notes
"Volume 246, Number 1164 (third of 6 numbers), March 2017."
The Physical Object
- Description:1 online resource (ix, 174 pages)
Edition Identifiers
- ISBN:9781470436377, 147043637X
- oclc:ocn968214336
- LC Classification:QA313
- Dewey Decimal:515/.48
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