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 …

This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This
includes the construction of branching foliations and leaf conjugacies on three-dimensional …

We prove that stable ergodicity is C r open and dense among conservative partially
hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2, infty]. The …

A non-dynamically coherent example on T3 - ScienceDirect Skip to main contentSkip to article
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These are notes for a minicourse in the School on Dynamical Systems 2015 at ICTP. This
version is quite preliminary, incomplete (mainly in the last sections) and probably contains …

We show the existence of a family of manifolds on which all (pointwise or absolutely)
partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds …

Let M be a smooth, connected, compact 3-dimensional Riemannian manifold without
boundary (a concrete choice of Riemannian metric is of no importance for the sequel). AC 1 …

In statistical physics, the Boltzmann–Maxwell ergodic hypothesis, designed to help describe
equilibrium and nonequilibrium systems of many particles, prompted a search for ergodic …

Some of the guiding problems in partially hyperbolic systems are the following:(1)
Examples,(2) Properties of invariant foliations,(3) Accessibility,(4) Ergodicity,(5) Lyapunov …

If a partially hyperbolic diffeomorphism on a torus of dimension has stable and unstable
foliations which are quasi-isometric on the universal cover, and its centre direction is one …