The Lorenz Attractor is Mixing Page 1 Digital Object Identifier (DOI) 10.1007/s00220-005-1411-9
Commun. Math. Phys. 260, 393–401 (2005) Communications in Mathematical Physics The …

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary
dimension, possibly having discontinuities and/or critical sets, and show that under some …

The long-term average response of observables of chaotic systems to dynamical
perturbations can often be predicted using linear response theory, but not all chaotic …

We prove that every geometric Lorenz attractor satisfying a strong dissipativity condition has
superpolynomial decay of correlations with respect to the unique Sinai–Ruelle–Bowen …

We prove that any C1+α transformation, possibly with a (non-flat) critical or singular region,
admits an invariant probability measure absolutely continuous with respect to any …

Local bifurcations of stationary points and limit cycles have successfully been characterized
in terms of the critical exponents of these solutions. Lyapunov exponents and their …

Critical intermittency stands for a type of intermittent dynamics in iterated function systems,
caused by an interplay of a superstable fixed point and a repelling fixed point. We consider …

The task of modeling and forecasting a dynamical system is one of the oldest problems, and
it remains challenging. Broadly, this task has two subtasks: extracting the full dynamical …

We claim that looking at probability distributions of finite time largest Lyapunov exponents,
and more precisely studying their large deviation properties, yields an extremely powerful …

We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate
critical and singular points admits an induced Markov tower with exponential return time …