Lap number entropy formula for piecewise affine and projective maps in several dimensions

Yutaka Ishii, Duncan Sands

Research output: Contribution to journalArticle

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2755-2772
Number of pages18
Issue number12
Publication statusPublished - Dec 1 2007


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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