Research

Graduate Student Colloquium

A fixed point theorem for twist maps

  • Speaker: Peizheng Yu (SUSTech)

  • Time: Jan 17, 2024, 19:00-19:40

  • Location: M5024, College of Science Bldg.

Abstract: Poincare's last geometric theorem 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 Poincare's geometric theorem, our result also has some applications to reversible systems.

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