Infinitesimal bending and twisting in one-dimensional dynamics

Author:
Frederick P. Gardiner

Journal:
Trans. Amer. Math. Soc. **347** (1995), 915-937

MSC:
Primary 30C65; Secondary 30F30, 30F60, 32G15, 47B99

DOI:
https://doi.org/10.1090/S0002-9947-1995-1290717-4

MathSciNet review:
1290717

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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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DOI:
https://doi.org/10.1090/S0002-9947-1995-1290717-4

Article copyright:
© Copyright 1995
American Mathematical Society