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The Fixed Points of an Analytic Self-Mapping
S. D. Fisher and John Franks
Proceedings of the American Mathematical Society
Vol. 99, No. 1 (Jan., 1987), pp. 76-78
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2046274
Page Count: 3
You can always find the topics here!Topics: Mathematical theorems, Riemann surfaces, Analytic functions, Conformity, Mathematical functions, Analytics, Automorphisms, Mathematical surfaces, Mathematics
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Let R be a hyperbolic Riemann surface embedded in a compact Riemann surface of genus g and let f be an analytic function mapping R into R, f not the identity function. Then f has as most 2g + 2 distinct fixed points in R; equality may hold. If f has 2 or more distinct fixed points, then f is a periodic conformal automorphism of R onto itself. This paper contains a proof of this theorem and several related results.
Proceedings of the American Mathematical Society © 1987 American Mathematical Society