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 reviews some basic mathematical results on Lyapunov exponents, one of the
most fundamental concepts in dynamical systems. The first few sections contain some very …

In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity k should display a power spectrum along an inertial range contained in …

We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of
the stochastically-forced 2D Navier–Stokes equations and 3D hyper-viscous Navier–Stokes …

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 …

The anti-integrable limit is one of the convenient and relatively simple methods for the
construction of chaotic hyperbolic invariant sets in Lagrangian, Hamiltonian, and other …

The phenomenon of the generic coexistence of infinitely many periodic orbits with different
numbers of positive Lyapunov exponents is analysed. Bifurcations of periodic orbits near a …

An exact solution of Einstein's equations which represents a pair of accelerating and rotating
black holes (a generalized form of the spinning C-metric) is presented. The starting point is a …

We show that maps with homoclinic tangencies of arbitrarily high orders and, as a
consequence, with arbitrarily degenerate periodic orbits are dense in the Newhouse regions …

We give an introduction to some of the numerical aspects in quantum chaos. The classical
dynamics of two-dimensional area-preserving maps on the torus is illustrated using the …