Complex Brjuno functions

Brjuno Numbers and Complex Dynamics

Brjuno Numbers and the Symbolic Dynamics of the Complex Exponential

In this paper, we note a connection between number theory and dynamical systems, in that we will show an object which is associated to a given family of analytic maps also has an interesting number theoretic property. It was shown in [DeV01] that there is a set of irrational numbers which are associated with the complex exponential family λe. We will show below that this set is closely related ...

Generalized Brjuno functions associated to α-continued fractions

For 0 ≤ α ≤ 1 given, we consider the α-continued fraction expansion of a real number obtained by iterating the map Aα(x) = ̨̨ x − ˆ x + 1− α ̃ ̨̨ defined on the interval Iα = (0, ᾱ), with ᾱ = max(α, 1− α). These maps generalize the classical (Gauss) continued fraction map which corresponds to the choice α = 1, and include the nearest integer (α = 1/2) and byexcess (α = 0) continued fraction expansio...

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Brjuno Condition and Renormalization for Poincaré Flows

In this paper we give a new proof of the local analytic linearisation of flows on T with a Brjuno rotation number, using renormalization techniques.