# David Martí-PeteUniversity of Liverpool | UoL · Department of Mathematical Sciences

David Martí-Pete

PhD Mathematics, The Open University

## About

8

Publications

537

Reads

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61

Citations

Citations since 2016

Introduction

My research area is Complex Dynamics which lies at the interplay of Complex Analysis and Dynamical Systems. More precisely, I study the iteration of transcendental entire functions and transcendental self-maps of the punctured plane.

Additional affiliations

October 2020 - present

December 2018 - September 2020

November 2016 - November 2018

Education

September 2013 - October 2016

September 2010 - October 2011

September 2006 - July 2010

## Publications

Publications (8)

We study the escaping set of functions in the class B*, that is, holomorphic functions f : C* → C* for which both zero and infinity are essential singularities, and the set of singular values of f is contained in an annulus. For functions in the class B*, escaping points lie in their Julia set. If f is a composition of finite order transcendental s...

We study the different rates of escape of points under iteration by
holomorphic self-maps of $\mathbb C^*=\mathbb C\setminus\{ 0\}$ for which both
0 and $\infty$ are essential singularities. Using annular covering lemmas we
construct different types of orbits, including fast escaping and arbitrarily
slowly escaping orbits to either 0, $\infty$ or b...

We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic functi...

We construct a transcendental entire function for which infinitely many Fatou components share the same boundary. This solves the long-standing open problem whether Lakes of Wada continua can arise in complex dynamics, and answers the analogue of a question of Fatou from 1920 concerning Fatou components of rational functions. Our theorem also provi...

We consider the dynamics of transcendental self-maps of the punctured plane, \(\mathbb {C}^*=\mathbb {C}{\setminus } \{0\}\). We prove that the escaping set \(I(f)\) is either connected, or has infinitely many components. We also show that \(I(f)\cup \{0,\infty \}\) is either connected, or has exactly two components, one containing 0 and the other...

We study the iteration of transcendental self-maps of $\mathbb{C}^*:=\mathbb{C}\setminus \{0\}$, that is, holomorphic functions $f:\mathbb{C}^*\to\mathbb{C}^*$ for which both zero and infinity are essential singularities. We use approximation theory to construct functions in this class with escaping Fatou components, both wandering domains and Bake...