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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290717-4
PII: S 0002-9947(1995)1290717-4
Article copyright: © Copyright 1995 American Mathematical Society