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

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)571-586
Number of pages16
JournalErgodic Theory and Dynamical Systems
Volume9
Issue number3
DOIs
Publication statusPublished - Sep 1989

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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