My principle research area is dynamical systems
theory and applications. A dynamical system consists of a manifold
whose points represent possible states of the system, "time" which may
be continuous or discrete, and the time-evolution law.
In some nonlinear systems similar initial states of the system lead to a very different future states. Such a phenomenon is known as chaos. As a consequence, the behavior of the system appears to be random despite the fact that system is deterministic.
Below is a gallery of strange attractors and fractals obtained by my students and me while conducting numerical experiments in dynamical systems.