Entropy of real rational surface automorphisms

We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{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 homol...

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Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Diller, Jeffrey, Kim, Kyounghee
Format: Article
Language:English
Subjects:
Automorphisms
Entropy
Homology
Online Access:Get full text
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Summary:We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{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.
ISSN:2331-8422