- 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 Ecalle-Hakim 's theorems in holomorphic dynamics
-
Index theorems for meromorphic self-maps 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 four-manifolds 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 for hyperbolic Riemann surface laminations I
Entropy for hyperbolic Riemann surface laminations I
- Chapter:
- (p.569) Entropy for hyperbolic Riemann surface laminations I
- Source:
- Frontiers in Complex Dynamics
- Author(s):
Tien-Cuong Dinh
Viet-Anh Nguyen
Nessim Sibony
, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland- Publisher:
- Princeton University Press
This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of the entropy. The chapter first focuses on compact laminations, which are transversally smooth, before turning to the case of singular foliations, showing how the Poincaré metric on leaves is transversally Hölder continuous. In addition, the chapter considers the problem in the proof that the entropy is finite for singular foliations is quite delicate and requires a careful analysis of the dynamics around the singularities. Finally, the chapter discusses a notion of metric entropy for harmonic probability measures and gives some open questions.
Keywords: entropy, Riemann surfaces, hyperbolic laminations, Poincaré metric, finiteness, compact laminations, singular foliations, metric entropy, harmonic probability measures
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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 Ecalle-Hakim 's theorems in holomorphic dynamics
-
Index theorems for meromorphic self-maps 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 four-manifolds 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
