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A projectively natural flow for circle diffeomorphisms. (English) Zbl 0773.58022

A certain flow given by a nonlinear fourth order PDE is investigated. The flow is motivated by a differential analogue of a geometric construction which gives a sequence of polygons. The author proves results concerning long term existence and uniqueness.
Reviewer: R.Cowen (Gaborone)

MSC:

37C10 Dynamics induced by flows and semiflows

Software:

Mathematica
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References:

[1] [G] Goldman, W.: Projective geometry on manifolds. Lecture Notes, University of Maryland, 1988 (available from the author)
[2] [H] Hamilton, R.: Harmonic maps of manifolds with boundary. (Lect. Notes math., vol. 471). Berlin Heidelberg New York: Springer 1975 · Zbl 0308.35003
[3] [N] Nehari, Z.: The Schwarzian derivative and schlicht functions. Bull. Am. Math. Soc.55 (1949) · Zbl 0035.05104
[4] [W] Wolfram, S. Mathematica: A system for doing mathematics by computer. Reading, MA: Addison Wesley 1988 · Zbl 0671.65002
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