Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

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
DOI: 10.2307/2046274
Stable URL: http://www.jstor.org/stable/2046274
Page Count: 3
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Fixed Points of an Analytic Self-Mapping
Preview not available

Abstract

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.

Page Thumbnails

  • Thumbnail: Page 
76
    76
  • Thumbnail: Page 
77
    77
  • Thumbnail: Page 
78
    78