Dynamics and Kinetics

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AbstractBunimovichThe proposal deals with the properties of finite- and infinite-dimensional dynamical systema. Both topological and ergodic properties are addressed. The systems under study include nonlinear hyperbolic partial differential equations, lattice dynamical systems (in particular, coupled map lattices), lattice gas cellular automata, billiards and the systems of interacting particles. The broad approach will be used that combines methods of the ergodic theory, the theory of nonuniformly hyperbolic dynamical systems and the theory of bifurcations.Most of the questions that will be addressed in this proposal have their origin in statistical physics, geometrical optics, hydrodynamics and biology and were transformed into the mathematical form by the principal investigator with collaborators. The new applications under study address the dynamical systems which naturally appear in manufacturing, especially in the dynamics of production lines. The application of ideas and methods of dynamical systems allowed already to increase production rates of such lines e.g. in the apparel industry. The major effort will be made now in the analysis of reentrant manufacturing systems which deal e.g. with the production od the semiconductors.