Discrete Holomorphic Local Dynamical Systems

Contents
Discrete Holomorphic Local Dynamical Systems ..................... 1
Marco Abate
1 Introduction .................................................... 1
2 One Complex Variable: The Hyperbolic Case ........................ 4
3 One Complex Variable: The Parabolic Case .......................... 9
4 One Complex Variable: The Elliptic Case ............................ 20
5 Several Complex Variables: The Hyperbolic Case ..................... 32
6 Several Complex Variables: The Parabolic Case ...................... 38
7 Several Complex Variables: Other Cases ............................ 49
References ........................................................ 50
Dynamics of Rational Surface Automorphisms ....................... 57
Eric Bedford
1 Polynomial Automorphisms of C 2 .................................. 57
1.1 Hénon Maps................................................ 57
1.2 Filtration .................................................. 59
1.3 Fatou Components .......................................... 62
1.4 Hyperbolicity ............................................... 65
1.5 Rate of Escape .............................................. 69
1.6 Böttcher Coordinate ......................................... 72
1.7 Currents on R N ............................................. 76
1.8 Currents on C N and Especially μ ± ............................. 78
1.9 Convergence to μ + .......................................... 82
2 Rational Surfaces ................................................ 83
2.1 Blowing Up ................................................ 83
2.2 Cohomology ............................................... 86
2.3 Invariant Currents and Measures ............................... 88
2.4 Three Involutions ........................................... 90
2.5 Linear Fractional Recurrences ................................. 94
2.6 Linear Fractional Automorphisms ............................. 96
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