Abstract

Several geometric and probabilistic methods for studying chaotic phase space transport have been developed and fruitfully applied to diverse areas from orbital mechanics to biomechanics to fluid mechanics and beyond. Increasingly, systems of interest are determined not by analytically defined model systems, but by data from experiments or large-scale simulations. This emphasis on real-world systems sharpens our focus on those features of phase space transport in finite-time systems which seem to be robust, leading to the consideration of not only invariant manifolds and invariant manifold-like objects, but also their connection with concepts such as symbolic dynamics, braids, and almost-invariant sets. This talk will address systems known analytically from which phase space structures controlling transport and stability can be computed, and approaches for identifying separatrices and quantifying transport in systems not known analytically. Applications to areas such as celestial mechanics, musculoskeletal biomechanics, ship capsize prediction, and atmospheric microbe transport will be discussed.