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Non-smooth geodesic flows and the earthquake flow on Teichmüller space*

Published online by Cambridge University Press:  19 September 2008

Howard Weiss
Howard Weiss
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, California 91125, U.S.A.
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Abstract

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Thurston generalized the notion of a twist deformation about a simple closed geodesic on a hyperbolic Riemann surface to a twisting or shearing along a much more complicated object called a measure geodesic lamination. This new deformation is called an earthquake and it generates a flow on the tangent bundle of Teichmüller space.

In this paper we study the earthquake flow. We show that the flow is not smooth and that it is not the geodesic flow for an affine connection. We also derive the explicit form of the system of differential equations which earthquake trajectories satisfy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 3 , September 1989 , pp. 571 - 586
Copyright
Copyright © Cambridge University Press 1989

References

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