Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping.
Real Koebe principle
We prove a version of the real Koebe principle for interval (or circle) maps with non-flat critical points.
Renormalization of exponential sums and matrix cocycles
In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics
Return time statistics for unimodal maps
We prove that a non-flat S-unimodal map satisfying a weak summability condition has exponential return time statistics on intervals around a.e. point. Moreover we prove that the convergence to the entropy in the Ornstein-Weiss formula enjoys normal fluctuations.
Reversibility in the diffeomorphism group of the real line.