A Real K3 Automorphism with Most of Its Entropy in the Real Part
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908392608497664 |
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| author | Cohen, Ethan |
| author_facet | Cohen, Ethan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Real K3 Automorphism with Most of Its Entropy in the Real Part Cohen, Ethan Dynamical Systems Algebraic Geometry 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. |
| title | A Real K3 Automorphism with Most of Its Entropy in the Real Part |
| topic | Dynamical Systems Algebraic Geometry |
| url | https://arxiv.org/abs/2506.03479 |