Georgia Institute of Technology College of Sciences

Dynamics of spatially extended systems is often described by Lattice Dynamical Systems (LDS). LDS were introduced 25 years ago independently by four physicists from four countries. Sometimes LDS themselves are quite relevant models of real phenomena. Besides, very often discretizations of partial differential equations lead to LDS. LDS consist of local dynamical systems sitting in the nodes of a lattice which interact between themselves. Mathematical studies of LDS started in 1988 and introduced a thermodynamic formalism for these spatially extended dynamical systems. They allowed to give exact definitions of such previously vague phenomena as space-time chaos and coherent structures and prove their existence in LDS. The basic notions and results in this area will be discussed.  It is a preparatory talk for the next day colloquium where Dynamical Networks, i.e.  the systems with arbitrary graphs of interactions, will be discussed.