Research in Dynamical Systems

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The proposal outlines a program of exploring different aspects of lowdimensional dynamics:combinatorial and geometric issues of holomorphic dynamics,its interplay with one-dimensional real dynamics (particularly in the rigidity and renormalization theories),interaction with three dimensional hyperbolic geometry and the theory offoliations, analytic and geometric aspects of two dimensional complex andreal dynamics.The dynamical systems theory studies the evolution of various systemsarising in physics, biology, engineering etc., as well as simplifiedmathematical models for those systems. It has been realized in the past 25years that even one- or two- dimensional models can exhibit rich andimportant phenomena. It has been also realized that the methods of complexanalysis provide powerful tools for dealing with these systems. Theproposal intends to explore further this branch of dynamics.