Papers › A Real K3 Automorphism with Most of Its Entropy in the Real Part
A Real K3 Automorphism with Most of Its Entropy in the Real Part
Ethan Cohen
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This article describes an example of a real projective K3 surface admitting a real automorphism f satisfying hₜₒₚ(f, X(ℂ)) < 2 hₜₒₚ(f, X(ℝ)). The example presented is a (2,2,2)-surface in ℙ¹ ×ℙ¹ ×ℙ¹ given by the vanishing set of (1 + x²)(1 + y²)(1 + z²) + 10xyz - 2, first considered by McMullen. Along the way, we develop an ad hoc shadowing lemma for C² (real) surface diffeomorphisms, and apply it to estimate the location of a periodic point in X(ℝ). This result uses the GNU MPFR arbitrary precision arithmetic library in C and the Flipper computer program.
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