New variational principles for locating periodic orbits of differential equations

Abstract

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier–Stokes equations, simulated using the lattice Boltzmann equation.