Mapping classes of Real Rational Surface Automorphisms
Kyounghee Kim

TL;DR
This paper studies the mapping classes of certain real rational surface automorphisms, revealing their pseudo-Anosov nature and providing a new geometric realization of Lehmer's number as a stretch factor.
Contribution
It determines the mapping classes of specific diffeomorphisms on real rational surfaces, showing they are pseudo-Anosov and not from Penner's construction, and realizes Lehmer's number as a stretch factor.
Findings
The diffeomorphisms are reducible with unique invariant curves.
Their restrictions are pseudo-Anosov and not from Penner's construction.
Lehmer's number is realized as the stretch factor for n=8.
Abstract
Let be a family of diffeomorphisms on real rational surfaces that are birationally equivalent to birational maps on . In this article, we investigate the mapping classes of the diffeomorphisms . These diffeomorphisms are reducible with unique invariant irreducible curves, and we determine the mapping classes of their restrictions, , on the cut surfaces, showing that they are pseudo-Anosov and do not arise from Penner's construction. For , Lehmer's number is realized as the stretch factor of , a pseudo-Anosov map on a once-punctured genus orientable surface. The diffeomorphism is a new geometric realization of a Lehmer's number.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals
