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 language | English (US) |
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Pages (from-to) | 4051-4059 |
Number of pages | 9 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 42 |
Issue number | 8 |
DOIs | |
State | Published - 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