{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-real-k3-automorphism-with-most-of-its","title":"A Real K3 Automorphism with Most of Its Entropy in the Real Part","arxiv_id":"2506.03479","date":"2025-06-04","proceeding":null,"authors":["Ethan Cohen"],"abstract":"This article describes an example of a real projective K3 surface admitting a real automorphism $f$ satisfying $h_{top}(f, X(\\mathbb{C})) < 2 h_{top}(f, X(\\mathbb{R}))$. The example presented is a $(2,2,2)$-surface in $\\mathbb{P}^1 \\times \\mathbb{P}^1 \\times \\mathbb{P}^1$ given by the vanishing set of $(1 + x^2)(1 + y^2)(1 + z^2) + 10xyz - 2$, first considered by McMullen. Along the way, we develop an ad hoc shadowing lemma for $C^2$ (real) surface diffeomorphisms, and apply it to estimate the location of a periodic point in $X(\\mathbb{R})$. This result uses the GNU MPFR arbitrary precision arithmetic library in C and the Flipper computer program.","url_abs":"https://arxiv.org/abs/2506.03479v1","url_pdf":"https://arxiv.org/pdf/2506.03479v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-real-k3-automorphism-with-most-of-its","repo_url":"https://github.com/ethanhcoo/k3entropy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}