A brief tour of nonlinear dynamics

Nonlinearity and chaos are ubiquitous and fascinating.  Chaotic systems, in particular, are exquisitely sensitive to small

perturbations, but their behavior has a fixed and highly characteristic pattern.  Making sense of this somewhat counterintuitive combination of effects is important to one's ability to understand the physical world.  I will begin this talk with a (very) light review of the core ideas of nonlinear dynamics, then move to descriptions of some of the ways in which one can put those ideas

into practice---nonlinear time-series analysis, information theory, and topological data analysis---with demonstration examples ranging from paleoclimate dynamics to music and dance.