Low-Dimensional and Symbolic Dynamics

Indiana University, Bloomington IN

Investigators

Abstract

Proposal Number: 0139916 PI: Michal Misiurewicz ABSTRACT The Principal Investigator will perform research in the theory of dynamical systems, mainly low-dimensional (both smooth and continuous) and symbolic. He will apply analytical, topological and combinatorial tools in order to investigate real and complex systems. A substantial part of the project is aimed at providing bridges between real and complex, one- and two-dimensional dynamics. A new class of two-dimensional systems will be considered. Quadratic laminations will be looked upon from the point of view of combinatorial dynamics and rotation theory. For other systems attractors, periodic orbits, rotation sets and topological entropy will be in the center of attention. Moreover, symbolic systems with an additional local order structure will be studied. For almost every phenomenon from Physics, Chemistry, Biology, Medicine, Economy and other sciences one can make a mathematical model that can be regarded as a dynamical system. Sometimes the study of this system is extremely difficult, but quite often it can be reduced to the study of a much simpler, low dimensional or symbolic one. This project is devoted mainly to the investigation of the properties of these types of systems from the mathematical point of view. The results that can be obtained are usually much stronger than in the general case and often lead to much deeper understanding of the original systems.