Infinitesimal bending and twisting in one-dimensional dynamics

Gardiner, Frederick P.

doi:10.1090/S0002-9947-1995-1290717-4

Infinitesimal bending and twisting in one-dimensional dynamics
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Trans. Amer. Math. Soc. 347 (1995), 915-937 Request permission

Abstract:

An infinitesimal theory for bending and earthquaking in one-dimensional dynamics is developed. It is shown that any tangent vector to Teichmüller space is the initial data for a bending and for an earthquaking ordinary differential equation. The discussion involves an analysis of infinitesimal bendings and earthquakes, the Hilbert transform, natural bounded linear operators from a Banach space of measures on the Möbius strip to tangent vectors to Teichmüller space, and the construction of a nonlinear right inverse for these operators. The inverse is constructed by establishing an infinitesimal version of Thurston’s earthquake theorem.

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