The topological entropy of a piecewise projective homeomorphism of the 2-sphere is shown to be given by the growth rate of the number of projective pieces under iteration, likewise for piecewise affine homeomorphisms of the plane. This is a two-dimensional version of the lap number formula for one-dimensional maps. In higher dimensions and for non-invertible maps we obtain only an inequality.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics