Rational Surface Automorphisms with Positive Entropy
نویسندگان
چکیده
منابع مشابه
Automorphisms of Rational Manifolds of Positive Entropy with Siegel Disks
Using McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.
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§0. Introduction. Cantat [C1] has shown that if a compact projective surface carries an automorphism of positive entropy, then it has a minimal model which is either a torus, K3, or rational (or a quotient of one of these). It has seemed that rational surfaces which carry automorphisms of positive entropy are relatively rare. Indeed, the first infinite family of such rational surfaces was found...
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§0. Introduction. Cantat [C1] has shown that if a compact projective surface carries an automorphism of positive entropy, then it has a minimal model which is either a torus, K3, or rational (or a quotient of one of these). It has seemed that rational surfaces which carry automorphisms of positive entropy are relatively rare. Indeed, the first infinite family of such rational surfaces was found...
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§0. Introduction. Let X denote a compact complex surface, and let f be a (biholomorphic) automorphism of X . The regular part of the dynamics of f occurs on the Fatou set F(f) ⊂ X , where the forward iterates are equicontinuous. As in [BS, U], we call a Fatou component U ⊂ F(f) a rotation domain of rank d if f |U generates a (real torus) T-action on U . In dimension 1, rotation domains correspo...
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Let X be a smooth projective surface over a number field K(⊂ C), and f : X → X an automorphism of positive topological entropy. In this paper, we show that there are only finitely many f -periodic curves on X . Then we define a height function ĥD corresponding to a certain nef and big R-divisor D on X and transforming well relative to f , and deduce some arithmetic properties of f -periodic poi...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2016
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.3014