Infinitesimal Bending and Twisting in One-dimensional Dynamics
نویسندگان
چکیده
An infinitesimal theory for bending and earthquaking in onedimensional dynamics is developed. It is shown that any tangent vector to Teichmuller 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 Mobius strip to tangent vectors to Teichmuller 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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