On Zeroes of the Schwarzian Derivative
نویسنده
چکیده
The main character of the present note is the Schwarzian derivative, and we start with a brief reminder of its definition and main properties. Let f : RP → RP be a projective line diffeomorphism. For every point x ∈ RP there exists a unique projective transformation gx : RP 1 → RP whose 2-jet at x coincides with that of f . The Schwarzian derivative S(f) measures the deviation of the 3-jet jf from jgx. More specifically, let x ∈ RP and v be a tangent vector to RP at x. Extend v to a vector field in a vicinity of x and denote by φt the corresponding local one-parameter group of diffeomorphisms. Consider 4 points:
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