Table of Contents

1. Nonautonomous flows as open dynamical systems: characterising escape rates and time-varying boundaries.
2. Eigenvalues of transfer operators for dynamical systems with holes.
3. Periodic points, escape rates and escape measures.
4. A multi-time step method to compute optical flow with scientific priors for observations of a fluidic system.
5. Numerical approximation of conditionally invariant measures via maximum entropy.
6. Lebesgue ergodicity of a dissipative subtractive algorithm.
7. Improved estimates of survival probabilities via isospectral transformations.
8. Dispersing billiards with small holes.
9. Almost-invariant and finite-time coherent sets: directionality, duration, and diffusion.
Return-time statistics, hitting-time statistics, and inducing. This book is comprised of selected research articles developed from a workshop onErgodic Theory, Probabilistic Methods and Applications, held in April 2012 at the BanffInternational Research Station.It contains contributions from world leading expertsin ergodic theory, dynamical systems, numerical analysis, fluid dynamics, and networks.The volume will serve asa valuable reference for mathematicians, physicists, engineers, physical oceanographers, atmospheric scientists, biologists, and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open, coherent, or non-equilibrium behavior.