简介

My core specialty field is Dynamical Systems. I do research in Chaos Theory and Control of Chaos, Time-Series Embedding Analysis, Frobenius-Perron Operators, Stochastic Dynamical Systems and Noise induced transport mechanism, Hamiltonian Dynamics, Symbol Dynamics, Celestial Mechanics, and Communicating with Chaos. I have been particularly interested in problems related to the fundamental issue in dynamical systems connected to model theory, regarding what constitutes a good model, leading us to develop mostly conjugacy. In particular, I have recently been working on how noise and determinism interact to create complication motions. I have also been working lately on image processing, particularly as related to observing and modeling dynamical systems from imagry, and information theoretic questions such as loss-less image compression as well as optimization and PDEs based methods of image denoising and image metrics. I am very interested in complex systems, and I run a networks/complex systems/nonlinear science/chaos group. I am interested in problems of model reduction, sensing, and predicting bursting as well as predicting nonstationarity. I am involved with airfoil flutter suppression in long aspect airfoils, with applications both to aircraft, specifically UAVs (unmanned air vehicles) and also to wind generated energy for controlling flutter and noise of large wind mills. Lately I have been particularly interested in problems in mixing and ecology regarding oceanography particularly as informed by remote sensing.