In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …

Résumé Depuis le travail fondamental de Poincaré sur l'étude qualitative des équations
différentielles en 1881, l'idée de chercher la description du comportement à long terme des …

Density of Hyperbolicity in Dimension One Page 1 Annals of Mathematics, 166 (2007), 145-182
Density of hyperbolicity in dimension one By O. Kozlovski, W. Shen, and S. van Strien 1 …

We consider smooth multimodal maps which have finitely many non-flat critical points. We
prove the existence of real bounds. From this we obtain a new proof for the non-existence of …

We prove that topologically conjugate non-renormalizable polynomials are quasi-
conformally conjugate. From this we derive that each such polynomial can be approximated …

We say that a rational function F satisfies the summability condition with exponent α if for
every critical point c which belongs to the Julia set J there exists a positive integer nc so that …

We prove an analog of Böttcher's theorem for transcendental entire functions in the
Eremenko–Lyubich class $\mathcal {B} $. More precisely, let f and g be entire functions with …

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and
van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove …

We prove exponential contraction of renormalization along hybrid classes of infinitely
renormalizable unimodal maps (with arbitrary combinatorics), in any even degree d. We …

In this paper, we study the dynamics of the Newton maps for arbitrary polynomials. Let p be
an arbitrary polynomial with at least three distinct roots, and f be its Newton map. It is shown …