Spectral Theory of Hamiltonian Dynamical Systems

哈密​​顿动力系统的谱理论

• 批准号: DP210101102
• 负责人: Prof Holger Dullin
• 金额: $ 21.79万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210101102
• 关键词: Spectral; Theory; Hamiltonian; Dynamical; Systems

Stability theory of steady states, travelling waves, periodic waves, and other coherent structures in nonlinear Hamiltonian partial differential equations is a cornerstone of modern dynamical systems. In particular it is of utmost importance to reliably compute eigenvalues, which determine the stability or instability of such structures. This project will develop methods to compute the spectrum of Hamiltonian operators in more than one spatial dimension. It will use the powerful geometric tools of the Maslov index and the Evans function. We will use these to simultaneously advance, and bring together the theories of the two dimensional Euler equations and Jacobi operators.

非线性汉密尔顿部分偏微分方程中稳态，行进波，周期性波和其他相干结构的稳定理论是现代动力学系统的基石。特别是可靠地计算特征值至关重要，这决定了这种结构的稳定性或不稳定。该项目将开发用于在一个以上的空间维度上计算哈密顿运营商的频谱的方法。它将使用Maslov索引的强大几何工具和Evans功能。我们将使用这些来同时推进，并将二维Euler方程和Jacobi操作员的理论汇总在一起。