Ergodic Theory and Area Preserving Mappings

  • Robert W. Easton
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 82)


Much work has been done recently in numerical (computer) studies of area preserving mappings of the plane. Often the orbit of a single point seems to fill a region in the plane having positive area. Such a region is called an “ergodic zone”. In this paper we give an exposition of some mathematical techniques which can be used to show that under suitable hypotheses, the closure of an orbit of a single point has positive Lebesque measure. We then apply these techniques to show that a family of mappings called linked twist maps are ergodic.


Ergodic Theory Unstable Manifold Orbit Structure Lyapunov Characteristic Exponent Lebesque Measure 
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Copyright information

© D. Reidel Publishing Company 1982

Authors and Affiliations

  • Robert W. Easton
    • 1
  1. 1.University of ColoradoBoulderUSA

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