This award supports two undergraduates working under the direction of the principal investigator on problems in mathematical analysis and dynamical systems. The work in analysis centers on geometric questions related to classes of continuous functions. Specifically, the students will consider compositions of continuous function and the structures one obtains by forming convex combinations of the compositions. The work expands earlier investigations with combinations of measure preserving transformations which occurs in the study of Markov operators. Investigations into dynamical systems will focus on recently developed ideas of pseudo-orbit shadowing. Shadowing measures the degree to which an orbit can be traced by nearby orbits. The phenomenon is important because dynamical systems with the shadowing property can be modeled on a computer. Students will be encouraged to present the results of their work at professional meetings.
