2007/10/03 by Katsunori Iwasaki, Iwasaki, Katsunori, Takato Uehara +1
Mathematics · #14E07 #37C25 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.0710.0706
openalex publication_date 2007/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that S. Saito's fixed point formula serves as a powerful tool for counting the number of isolated periodic points of an area-preserving surface map admitting periodic curves. His notion of periodic curves of types I and II plays a central role in our discussion. We establish a Shub-Sullivan type result on the stability of local indices under iterations of the map, the finiteness of the number of periodic curves of type II, and the absence of periodic curves of type I. Combined with these results, Saito's formula implies the existence of infinitely many isolated periodic points whose cardinality grows exponentially as period tends to infinity.