Dynamics of foliations
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Foliations of Riemannian manifolds can be considered as multidimensional dynamical systems: Riemannian structure (more precisely, Riemannian structure along the leaves) plays the role of time, the leaves play the role of orbits \cite{Walczak2004}. The dynamics of a foliation can be described in terms of its holonomy psudogroup (see [[Foliations#Holonomy]]). | Foliations of Riemannian manifolds can be considered as multidimensional dynamical systems: Riemannian structure (more precisely, Riemannian structure along the leaves) plays the role of time, the leaves play the role of orbits \cite{Walczak2004}. The dynamics of a foliation can be described in terms of its holonomy psudogroup (see [[Foliations#Holonomy]]). | ||
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Revision as of 13:40, 26 November 2010
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1 Introduction
Foliations of Riemannian manifolds can be considered as multidimensional dynamical systems: Riemannian structure (more precisely, Riemannian structure along the leaves) plays the role of time, the leaves play the role of orbits [Walczak2004]. The dynamics of a foliation can be described in terms of its holonomy psudogroup (see Foliations#Holonomy).
Pseudogroups
2 References
- [Walczak2004] P. Walczak, Dynamics of foliations, groups and pseudogroups, Birkhäuser Verlag, 2004. MR2056374 (2005d:57042) Zbl 1084.37022
