Some remarks on Birkhoff and Mather twist map theorems

Anatoly Katok

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A recent result of J. Mather [1] about the existence of quasi-periodic orbits for twist maps is derived from an appropriately modified version of G. D. Birkhoff's classical theorem concerning periodic orbits. A proof of Birkhoff's theorem is given using a simplified geometric version of Mather's arguments. Additional properties of Mather's invariant sets are discussed.

Original languageEnglish (US)
Pages (from-to)185-194
Number of pages10
JournalErgodic Theory and Dynamical Systems
Issue number2
Publication statusPublished - Jan 1 1982


All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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