# Bifurcation loci of families of finite type meromorphic maps

@inproceedings{Astorg2021BifurcationLO, title={Bifurcation loci of families of finite type meromorphic maps}, author={Matthieu Astorg and Anna Miriam Benini and N{\'u}ria Fagella}, year={2021} }

. We show that J − stability is open and dense in natural families of meromorphic maps of one complex variable with a ﬁnite number of singular values, and even more generally, to ﬁnite type maps . This extends the results of Mañé-Sad-Sullivan [MSS83] for rational maps of the Riemann sphere and those of Eremenko and Lyubich [EL92] for entire maps of ﬁnite type of the complex plane, and essentially closes the problem of density of structural stability for holomorphic dynamical systems in one…

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## References

SHOWING 1-10 OF 41 REFERENCES

### 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…

### On the Zeros of Solutions of Linear Differential Equations of the Second Order

- Mathematics
- 1998

Let u be a solution of the differential equation u″+Ru=0, where R is rational. Newton's method of finding the zeros of u consists of iterating the function f(z)=z−u(z)/u′(z). With suitable hypotheses…

### Complex Dynamics and Renormalization

- Mathematics
- 1994

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid…

### A separation theorem for entire transcendental maps

- Mathematics
- 2015

We study the distribution of periodic points for a wide class of maps, namely entire transcendental functions of finite order and with bounded set of singular values, or compositions thereof. Fix p∈N…

### Connectivity of Julia sets of Newton maps: a unified approach

- MathematicsRevista Matemática Iberoamericana
- 2018

In this paper we give a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function of the complex plane (a polynomial of degree large than $1$ or an entire…

### On the singularities of the inverse to a meromorphic function of finite order

- Mathematics, Philosophy
- 1995

Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ?, then every asymptotic value of f, except at most 2? of…

### Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)

- Mathematics
- 2009

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.…

### A finiteness theorem for a dynamical class of entire functions

- MathematicsErgodic Theory and Dynamical Systems
- 1986

Abstract We define a class Σ of entire functions whose covering properties are similar to those of rational maps. The set Σ is closed under composition of functions, and we show that when regarded as…

### Direct singularities and completely invariant domains of entire functions

- Mathematics, Philosophy
- 2006

Let f be a transcendental entire function which omits a point a ∈ C. We show that if D is a simply connected domain which does not contain a, then the full preimage f(D) is disconnected. Thus, in…

### Cycle doubling, merging, and renormalization in the tangent family

- MathematicsConformal Geometry and Dynamics of the American Mathematical Society
- 2018

In this paper we study the transition to chaos for the restriction to the real and imaginary axes of the tangent family
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