A FIXED POINT THEOREM FOR TWIST MAPS

Zhihong Xia, Peizheng Yu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Poincaré's last geometric theorem (Poincaré-Birkhoff Theorem [2]) states that any area-preserving twist map of annulus has at least two fixed points. We replace the area-preserving condition with a weaker intersection property, which states that any essential simple closed curve intersects its image under f at least at one point. The conclusion is that any such map has at least one fixed point. Besides providing a new proof to Poincaré's geometric theorem, our result also has some applications to reversible systems.

Original languageEnglish (US)
Pages (from-to)4051-4059
Number of pages9
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume42
Issue number8
DOIs
StatePublished - Aug 2022

Keywords

  • Poincaré's last geometric theorem
  • Poincaré-Birkhoff theorem
  • Twist maps
  • reversible maps

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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