- 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 II
Entropy for hyperbolic Riemann surface laminations II
- Chapter:
- (p.593) Entropy for hyperbolic Riemann surface laminations II
- 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 studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated singularities on a compact complex surface is finite. The chapter then proves the finiteness of the entropy in the local setting near a singular point in any dimension, using a division of a neighborhood of a singular point into adapted cells. Next, the chapter estimates the modulus of continuity for the Poincaré metric along the leaves of the foliation, using notion of conformally (R,δ)-close maps. The estimate holds for foliations on manifolds of higher dimension.
Keywords: entropy, Riemann surfaces, Riemann surface foliations, tame singular points, hyperbolic entropy, Brody hyperbolic foliation, compact complex surface, finiteness, Poincaré metric
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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
