Dynamics and Kinetics

摘要本文讨论了有限维和无限维动力系统的性质。讨论了拓扑和遍历性质。所研究的系统包括非线性双曲偏微分方程、晶格动力系统（特别是耦合映射晶格）、晶格气体细胞自动机、台球和相互作用粒子系统。我们将采用广泛的方法，结合遍历理论、非均匀双曲动力系统理论和分岔理论。在本提案中将要解决的大多数问题都起源于统计物理学、几何光学、流体力学和生物学，并由首席研究员及其合作者转化为数学形式。所研究的新应用解决了在制造业中自然出现的动态系统，特别是在生产线的动态中。动力系统的思想和方法的应用已经允许提高这类生产线的生产率，例如在服装行业。现在的主要工作将放在分析可重入制造系统上，例如处理半导体的生产。

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.