Dynamical systems are all around us. Any physical phenomenon can be described as either stochastic or deterministic dynamics. Understanding of the dynamics’ geometry and structure is crucial to any applications.
In my master’s, we developed control and guidance systems for an F16 simulator in autonomous flights and air combats. In my Ph.D., we generalized the concept of spectral decomposition by finding the dynamical modes of nonlinear diffusion. In both disciples, the main contribution was to find the relation to the linear systems. My research interest is to find relations between linear and nonlinear phenomena and thus to find their parsimonious representations.
The applications on my theory can be found in Image Processing, Data Mining from the perspective of Dynamics.
