 Title Pages
 Preface
 Introduction

Arithmetic of Unicritical Polynomial Maps
 Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques

Dynamical cores of topological polynomials

The quadratic dynatomic curves are smooth and irreducible
 Multicorns are not path connected

Leading monomials of escape regions

Limiting behavior of Julia sets of singularly perturbed rational maps
 On (non)local connectivity of some Julia sets

Perturbations of weakly expanding critical orbits
 Unmating of rational maps: Sufficient criteria and examples
 A framework toward understanding the characterization of holomorphic dynamics
 Metric stability for random walks (with applications in renormalization theory)
 Milnor's conjecture on monotonicity of topological entropy: Results and questions
 Entropy in dimension one

On EcalleHakim 's theorems in holomorphic dynamics

Index theorems for meromorphic selfmaps of the projective space
 Dynamics of automorphisms of compact complex surfaces
 Bifurcation currents and equidistribution in parameter space
 Entropy for hyperbolic Riemann surface laminations I
 Entropy for hyperbolic Riemann surface laminations II

Intersection theory for ergodic solenoids
 Invariants of fourmanifolds with flows via cohomological field theory

Two papers which changed my life: Milnor's seminal work on flat manifolds and bundles

Mil nor's problem on the growth of groups and its consequences
 Contributors
 Index
Index theorems for meromorphic selfmaps of the projective space
Index theorems for meromorphic selfmaps of the projective space
 Chapter:
 (p.451) Index theorems for meromorphic selfmaps of the projective space
 Source:
 Frontiers in Complex Dynamics
 Author(s):
Marco Abate
, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland Publisher:
 Princeton University Press
This chapter uses techniques from the theory of local dynamics of holomorphic germs tangent to the identity to prove three index theorems for global meromorphic maps of projective space. More precisely, the chapter seeks to prove a particular index theorem: Let f : ℙⁿ ⇢ ℙⁿ be a meromorphic selfmap of degree ν + 1 ≥ 2 of the complex ndimensional projective space. Let Σ(f) = Fix(f) ∪ I(f) be the union of the indeterminacy set I(f) of f and the fixed points set Fix(f) of f. Let Σ(f) = ⊔subscript Greek Small Letter AlphaΣsubscript Greek Small Letter Alpha be the decomposition of Σ in connected components, and denote by N the tautological line bundle of ℙⁿ. After laying out the statements under this theorem, the chapter discusses the proofs.
Keywords: index theorems, local dynamics, holomorphic germs, global meromorphic maps, projective space, decomposition
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 Title Pages
 Preface
 Introduction

Arithmetic of Unicritical Polynomial Maps
 Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques

Dynamical cores of topological polynomials

The quadratic dynatomic curves are smooth and irreducible
 Multicorns are not path connected

Leading monomials of escape regions

Limiting behavior of Julia sets of singularly perturbed rational maps
 On (non)local connectivity of some Julia sets

Perturbations of weakly expanding critical orbits
 Unmating of rational maps: Sufficient criteria and examples
 A framework toward understanding the characterization of holomorphic dynamics
 Metric stability for random walks (with applications in renormalization theory)
 Milnor's conjecture on monotonicity of topological entropy: Results and questions
 Entropy in dimension one

On EcalleHakim 's theorems in holomorphic dynamics

Index theorems for meromorphic selfmaps of the projective space
 Dynamics of automorphisms of compact complex surfaces
 Bifurcation currents and equidistribution in parameter space
 Entropy for hyperbolic Riemann surface laminations I
 Entropy for hyperbolic Riemann surface laminations II

Intersection theory for ergodic solenoids
 Invariants of fourmanifolds with flows via cohomological field theory

Two papers which changed my life: Milnor's seminal work on flat manifolds and bundles

Mil nor's problem on the growth of groups and its consequences
 Contributors
 Index