arXiv subjects

Peizheng Yu

Publications and source records attributed to Peizheng Yu.

2 recordsLinked to original sources

arXiv2024

A Simple Example of Pathological Foliations in Skew-Product Diffeomorphisms

Inspired by examples of Katok and Milnor \cite{Milnor1997}, we construct simple examples of skew-product volume preserving diffeomorphism where the center foliation is pathological in the sense that, there is a full measure set whose intersection with any center leaf contains at most one point. Comparing with other examples in literature, our mechanism for producing such pathological foliation is simple and elementary.

math.DS↗

arXiv2021

A fixed point theorem for twist maps

Poincare's last geometric theorem (Poincare-Birkhoff 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.

math.DS↗