Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

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

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

We prove exponential decay of correlations for a class of C^ 1+ α C 1+ α uniformly
hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular …

" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

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 display a gallery of Lorenz-like attractors that emerge in a class of three-dimensional
maps. We review the theory of Lorenz-like attractors for diffeomorphisms (as opposed to …

We prove the existence of a contracting invariant topological foliation in a full
neighbourhood for partially hyperbolic attractors. Under certain bunching conditions, it can …

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 …

We prove for a generic star vector field $ X $ that, if for every chain recurrent class $ C $ of $
X $ all singularities in $ C $ have the same index, then the chain recurrent set of $ X $ is …