Dynamics and Kinetics

Bunimovich的建议涉及有限维和无限维动力系统的性质。拓扑和遍历性质的解决。 所研究的系统包括非线性双曲型偏微分方程、格子动力系统（特别是耦合映象格子）、格子气细胞自动机、台球和相互作用粒子系统。将使用广泛的方法，结合遍历理论的方法，非均匀双曲动力系统的理论和理论的bifurcations.Most的问题，将解决在这个建议有其起源的统计物理学，几何光学，流体力学和生物学，并转化为数学形式的首席研究员与合作者。正在研究的新应用解决了在制造业中自然出现的动态系统，特别是生产线的动态。动态系统的思想和方法的应用已经允许增加这种生产线的生产率，例如在服装行业中。现在主要的工作是分析可重入制造系统，例如半导体的生产。

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.