A simple proof of polar decomposition in pseudo-Euclidean geometry
We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry.
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Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows
Artur Avila, Marcelo Viana, Amie Wilkinson (2015)
Journal of the European Mathematical Society
We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.
Abundance of hyperbolicity in the topology
Raúl Ures (1995)
Annales scientifiques de l'École Normale Supérieure
Asymptotic windings over the trefoil knot.
Jacques Franchi (2005)
Revista Matemática Iberoamericana
Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms.Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which is the asymptotic homology performed by the Brownian motion in G/Γ', describing thereby in an intrinsic way part...
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