Equilibrium measures for transcendental dynamics
speaker: Han Peters (University of Amsterdam)abstract: In ongoing work with Leandro Arosio, Anna Miriam Benini and John Erik Fornaess, we study the entropy of transcendental maps, both in one and two variables. Following a suggestion of Nessim Sibony, we aim to prove that the entropy of transcendental maps is infinite. In previous work we treated topological entropy. In current work we aim to construct analogues of the unique measure of maximal entropy for rational maps.
For rational maps, the unique measure of maximal entropy can be constructed in a number of different ways: via equidistribution of preimages or periodic cycles, by taking the Laplacian of the Green's function for polynomials, and for particularly nice maps, by using symbolic dynamical systems. None of these methods easily generalize to arbitrary transcendental maps. In this talk I will discuss different one-dimensional transcendental functions for which either symbolic dynamics or equidistribution methods lead to ergodic measures of infinite entropy. For these examples the support of the measure equals the entire Julia set.
timetable:
Wed 29 May, 10:30 - 11:20, Aula Dini
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