 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
Entropy in dimension one
Entropy in dimension one
 Chapter:
 (p.339) Entropy in dimension one
 Source:
 Frontiers in Complex Dynamics
 Author(s):
William P. Thurston
, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland Publisher:
 Princeton University Press
This chapter studies the topological entropy h of postcritically finite onedimensional maps and, in particular, the relations between dynamics and arithmetics of eʰ, presenting some constructions for maps with given entropy and characterizing what values of entropy can occur for postcritically finite maps. In particular, the chapter proves: h is the topological entropy of a postcritically finite interval map if and only if h = log λ, where λ ≥ 1 is a weak Perron number, i.e., it is an algebraic integer, and λ ≥ ∣λsuperscript Greek Small Letter Sigma∣ for every Galois conjugate λsuperscript Greek Small Letter Sigma ∈ C. Unfortunately, the author of this chapter has died before completing this work, hence this chapter contains both the original manuscript as well as a number of notes which clarify many of the points mentioned therein.
Keywords: topological entropy, onedimensional maps, dynamics, arithmetics, entropy, postcritically finite maps, topological space
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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