Periodic points of endperiodic maps. Preprint, 2024. PDF. ArXiv link. To appear in Groups, Geometry, and Dynamics.
Abstract: Let g : L → L be an atoroidal, endperiodic map on an infinite type surface L with no boundary and finitely many ends, each of which is accumulated by genus. By work of Landry, Minsky, and Taylor, g is isotopic to a spun pseudo-Anosov map f. We show that spun pseudo-Anosov maps minimize the number of periodic points of period n for sufficiently high n over all maps in their homotopy class, strengthening a theorem of Landry, Minsky, and Taylor. We also show that the same theorem holds for atoroidal Handel--Miller maps when one only considers periodic points that lie in the intersection of the stable and unstable laminations. Furthermore, we show via example that spun-pseudo Anosov and Handel--Miller maps do not always minimize the number of periodic points of low period.