We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting some quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to understand how the real part of an automorphism acts on homology. We apply this understanding to give examples where the entropy of the full (complex) automorphism is the same as its real restriction. Conversely and by different methods, we exhibit different examples where the entropy is strictly decreased by restricting to the real part of the surface. Finally, we give an example of a rational surface automorphism with positive entropy whose periodic cycles are all real.
机构:
CNRS, IRMAR, UMR 6625, F-35042 Rennes, France
Univ Rennes 1, F-35042 Rennes, France
Ecole Normale Super, CNRS, DMA, UMR 8553, F-75230 Paris 05, FranceCNRS, IRMAR, UMR 6625, F-35042 Rennes, France
Cantat, Serge
Dolgachev, Igor
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机构:
Univ Michigan, Dept Math, Ann Arbor, MI 49109 USACNRS, IRMAR, UMR 6625, F-35042 Rennes, France