9619881 This award is for support of a conference/workshop in dynamical systems at the Department of Mathematics of the University of North Texas. Speakers at the workshop will include Professors Katok (Penn State), Keane (CWI, Amsterdam), Przytycki (IM PAN, Warsaw) and Strein (University of Amsterdam). Participants in the workshop will include scholars form the Southwestern US and Northern Mexico. Dynamical systems theory describes processes that develop over time. In particular, dynamical systems arise in physics (Lorenz map), biology and environmental studies (population dynamics) and chemistry (e.g. modeling the Belousov-Zhabotinskii reaction). The development of the system depends on its initial state and parameters coming from the "environment." It is of great importance that we understand the future behavior which may be exhibited by the system for the "majority" of its initial states; this corresponds to the description of so-called attractors to which the first part of the project is devoted. Also in the first part of the proposal we study how properties of some important dynamical systems depend on "environmental" parameters. Sometimes phenomena exhibited by a system are related to one another and information about some of them allows one to make a judgment about the existence of others; in other words phenomena coexist. A good example here is periodicity, i.e. cyclic occurrence of the same states in the system. It turns out that the existence of a cyclic process with a given period for some initial state guarantees that another cyclic process with a different period can be realized for a different initial state and the same environment. In the second part of the project we plan to thoroughly study this relationship between different periods of cyclic processes in the same system.
