Dynamics, Patterns and Symmetry

小行星9704980 偏微分方程中螺旋波和胞腔模式的分支 将研究圆盘上的方程。 无界 域、螺旋波和涡卷波的分叉和曲折以及 Ginzburg-Landau理论的空间扩展系统将被考虑-与应用程序的空间非周期性的解决方案，在空间扩展 系统. 此外，部分工作将用于研究 动力学存在于对称的常微分方程中。 稳定 连续对称问题中混沌吸引子的遍历性， 鲁棒异宿环的存在性、稳定性和分支性， 研究了 其中一些想法与间歇式磁力发电机有关 在旋转对流中。 模式出现在物理、化学和生物系统中， 突出的和可复制的特点。 因此，科学家和 数学家们已经发展出理论来解释这些 模式. 有几种方法来研究模式;这一个是 基于对称性和分叉。 建议对该理论进行研究 对称动力系统及其与模式的关系 阵 分析中存在根本差异， 所研究的模式是否完全适合有界域， 边界是否不重要，方程是否在无穷大上 域.这两种情况的各个方面都将得到研究。

9704980 Golubitsky Bifurcations to spiral waves and to cellular patterns in partial differential equations posed on a circular disk will be investigated. In unbounded domains, the bifurcation and meandering of spirals and scroll waves and the Ginzburg-Landau theory of spatially extended systems will be considered -- - with application to spatially aperiodic solutions in spatially extended systems. In addition, part of the effort will be devoted to studying the dynamics present in ordinary differential equations with symmetry. Stable ergodicity of chaotic attractors in problems with continuous symmetry, and the existence, stability and bifurcations of robust heteroclinic cycles will be studied. Some of these ideas are relevant to intermittent magnetic dynamos in rotating convection. Patterns appear in physical, chemical, and biological systems and are characteristically striking and reproducible. Consequently, scientists and mathematicians have developed theories to explain the origins of these patterns. There are several approaches to the study of pattern; this one is based on symmetry and bifurcation. It is proposed to investigate the theory and application of symmetric dynamical systems and its relation to pattern formation. There are fundamental differences in the analyses depending on whether the patterns being studied fit neatly into a bounded domain or whether boundaries are unimportant and the equations are posed on infinite domains. Aspects of both cases will be studied.