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Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
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Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

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Dynamics of automorphisms of compact complex surfaces

Dynamics of automorphisms of compact complex surfaces

Chapter:
(p.463) Dynamics of automorphisms of compact complex surfaces
Source:
Frontiers in Complex Dynamics
Author(s):

Serge Cantat

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159294.003.0018

This chapter describes the dynamics of automorphisms of compact complex surfaces when it is rich. In particular, the chapter carries to this general setting the interplay between ideas from ergodic and pluripotential theories. The study is restricted to compact Kähler surfaces. This is justified by the fact that the topological entropy of all automorphisms vanishes on compact complex surfaces which are not Kähler. Moreover, no proof is detailed in this chapter, but a few arguments are sketched in order to enlighten the interplay between algebraic geometry, complex analysis, and dynamical systems. Furthermore, when a result holds for automorphisms of projective surfaces over any algebraically closed field k, the chapter mentions it.

Keywords:   automorphisms, compact complex surfaces, ergodic theories, pluripotential theories, compact Kähler surfaces, algebraic geometry, complex analysis, dynamical systems, projective surfaces

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