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On the dynamics of the automorphism group of \(K3\) surfaces. (Sur la dynamique du groupe d’automorphismes des surfaces \(K3\).) (French) Zbl 1081.14513
Summary: We study the dynamics of the automorphism groups of \(K3\) surfaces. Assuming that the surface contains two elliptic fibrations that are invariant by non-periodic automorphisms, we give the classification of invariant probability measures. We also describe the closure of orbits and then give applications to the repartition of rational points on \(K3\) surfaces.

MSC:
14J28 \(K3\) surfaces and Enriques surfaces
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
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