A Continuous Mapping That Fixes All Boundary Points but No Interior Points

Except for the zero shift, each member of this family of continuous mappings of the unit disk into itself fixes the boundary pointwise but has no interior fixed points. (The point is a fixed point of if ) The method used is to map the interior of the disk to the whole plane with , translate by the shift, and map back to the disk with .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.