# Dynamics of automorphisms of compact complex surfaces

# Dynamics of automorphisms of compact complex surfaces

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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