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 …

Rigidity is a fundamental phenomenon in hyperbolic geometry and holomorphic dynamics.
Its meaning is that the metric properties of certain manifolds or dynamical systems are …

In this paper we complete a program to study measurable dynamics in the real quadratic
family. Our goal was to prove that almost any real quadratic map, c∈[-2, 1/4], has either an …

In this paper we prove that in any non-trivial real analytic family of quasiquadratic maps,
almost any map is either regular (ie, it has an attracting cycle) or stochastic (ie, it has an …

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to
the permutation entropy. The conditional entropy of ordinal patterns describes the average …

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 …

We prove that almost every nonregular real quadratic map is Collet-Eckmann and has
polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that …

This is a continuation of notes on dynamics of quadratic polynomials. In this part we transfer
the geometric result of [L3] to the parameter plane. To any parameter value c GM in the …

Page 1 Springer ALBERTO A. PINTO DAVID A. RAND FLÁVIO FERREIRA Fine Structures of
Hyperbolic Diffeomorphisms Springer Monographs in Mathematics Page 2 Springer Monographs …

In the last quarter of the twentieth century the real quadratic family fc: R→ R, fc: x↦→ x2+ c
(c∈ R) was recognized as a very interesting and representative model of chaotic dynamics …