It is well known that in a small neighbourhood of a parabolic fixed point a real-analytic diffeomorphism of (R2, 0) embeds in a smooth autonomous flow. In this paper we show that the complex-analytic situation is completely different and a generic diffeomorphism cannot be embedded in an analytic flow in a neighbourhood of its parabolic fixed point. We study two analytic invariants with respect ...

Zeros of Random Analytic Functions The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of generality. We study zeros of random analytic functions in one complex variable. It is known that there is a one parameter family o...

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytic separate sets in R2, and we can definably analytic approximate definable continuous unary functions.