Mathematical Sciences: Problems of Dynamical System Theory

约翰·古肯海默将在多个不同领域开展研究。这些问题包括一维映射、平面上的二次向量场和多重分叉。他已经在所有这些领域确立了自己的国际领袖地位。目前的提议是这一非常成功的计划的延续。在过去的十年中，一维映射迭代的数学理论得到了迅速的发展。这一理论已经成功地应用于化学反应理论、半导体器件动力学和流体动力学中的混沌行为转变等多个领域。古肯海默在与其他领域的科学家互动方面有着良好的记录。他对多重分叉的研究旨在对发生在二次哈密顿系统附近的退化分叉类型进行分类。这将被用来寻找希尔伯特第16个问题的受限形式的解决方案。

John Guckenheimer will carry out research in a number of different areas. These include one dimensional mappings, quadratic vector fields in the plane and multiple bifurcations. He has already established himself as an international leader in all of these areas. The current proposal is a continuation of this very successful program. Over the last decade there has been a rapid growth in the mathematical theory of iterations of one dimensional mappings. This theory has been successfully applied in such diverse areas as the theory of chemical reactors, the dynamics of semiconductor devices and the transition to chaotic behaviour in fluid dynamics. Guckenheimer has a good record of interaction with scientists in other fields. His research into multiple bifurcations will be aimed at classifying types of degenerate bifurcations which occur near quadratic Hamiltonian systems. This will be used to find solutions to a restricted form of Hilbert's 16th problem.