# Bounded geometry and characterization of some transcendental maps

@article{Keen2017BoundedGA, title={Bounded geometry and characterization of some transcendental maps}, author={Linda Keen and Tao Chen and Yunping Jiang}, journal={Indiana University Mathematics Journal}, year={2017}, volume={66}, pages={1537-1571} }

We define two classes of topological infinite degree covering maps modeled on two families of transcendental holomorphic maps. The first, which we call exponential maps of type (p, q), are branched coverings and is modeled on transcendental entire maps of the form Pe, where P and Q are polynomials of degrees p and q. The second is the class of universal covering maps from the plane to the sphere with two removed points modeled on transcendental meromorphic maps with two asymptotic values. The…

## 3 Citations

Stable components in the parameter plane of meromorphic functions of finite type

- Mathematics
- 2017

We study the parameter planes of certain one-dimensional, dynamically-defined slices of holomorphic families of meromorphic transcendental maps of finite type for which infinity is not an asymptotic…

Dynamics of purely meromorphic functions of bounded type

- Mathematics
- 2017

We study the parameter plane of one-dimensional dynamically defined slices of meromorphic transcendental maps of finite type for which infinity is not an asymptotic value. More precisely we…

Stable Components in the Parameter Plane of Transcendental Functions Of Finite Type

- Mathematics
- 2017

We study the parameter planes of certain one-dimensional, dynamically-defined slices of holomorphic families of entire and meromorphic transcendental maps of finite type. Our planes are defined by…

## References

SHOWING 1-10 OF 20 REFERENCES

Bounded Geometry and Families of Meromorphic Functions with Two Asymptotic Values

- Mathematics
- 2011

In this paper we consider the topological class, denoted byAV2, of universal covering maps from the plane to the sphere with two removed points. We prove that an element f2AV2 with nite post-singular…

On Siegel disks of a class of entire maps

- Mathematics
- 2010

Let f : C → C be an entire map of the form f(z) = P(z)exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we…

Exponential Thurston maps and limits of quadratic differentials

- Mathematics
- 2008

Contents 1. Introduction 2 Organization of the paper 3 2. The characterization theorem 4 2.1. Definitions and statement of the main theorem 4 2.2. Classification of postsingularly finite exponential…

Quasiconformal surgery in holomorphic dynamics

- Medicine
- 2013

This book discusses surgery and its applications in dynamical systems and actions of Kleinian groups, as well as some of the principles of surgery as applied to extensions and interpolations.

Canonical Thurston Obstructions for Sub-Hyperbolic Semi-Rational Branched Coverings

- Mathematics
- 2011

We prove that the canonical Thurston obstruction for a sub-hyperbolic semi-rational branched covering exists if the branched covering is not CLH-equivalent to a rational map.

Analytic Functions

- MathematicsNature
- 1962

Analytic FunctionsBy R. Nevanlinna, H. Behnke and H. Grauert, L. V. Ahlfors, D. C. Spencer, L. Bers, K. Kodaira, M. Heins, J. A. Jenkins. (Princeton Mathematical Series, No. 24.) Pp. vii + 197.…

Ordinary Differential Equations In The Complex Domain

- Mathematics
- 2016

Thank you very much for reading ordinary differential equations in the complex domain, maybe you have knowledge that, people have look hundreds of times for their chosen readings like this, but end up in infectious downloads.

A framework towards understanding the characterization of holomorphic maps (with an appendix

- 2014

A framework towards understanding the characterization of holomorphic maps (with an appendix by Tao Chen, Yunping Jiang, and Linda Keen)

- Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday
- 2014