Geodesic flows on the Bott-Virasoro group with Dubinskii norm.

Guha, Partha

Displaying similar documents to “Geodesic flows on the Bott-Virasoro group with Dubinskii norm.”

Ito equation as a geodesic flow on $\hat{{Diff}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$

Partha Guha (2000)

Archivum Mathematicum

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The Ito equation is shown to be a geodesic flow of $L^{2}$ metric on the semidirect product space $\hat{{𝐷𝑖𝑓𝑓}^{s} (S^{1}) ⨀ C^{\infty} (S^{1})}$ , where ${𝐷𝑖𝑓𝑓}^{s} (S^{1})$ is the group of orientation preserving Sobolev $H^{s}$ diffeomorphisms of the circle. We also study a geodesic flow of a $H^{1}$ metric.

Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

Artur Avila, Marcelo Viana, Amie Wilkinson (2015)

Journal of the European Mathematical Society

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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.