Indexing domains of instability for Hamiltonian systems
Indexing domains of instability for Hamiltonian systems
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DOI：
10.1007/s000300050057
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发表时间：
1998-11
期刊：
影响因子：
--
通讯作者：
Y. Long;Tianqing An
中科院分区：
文献类型：
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作者：
Y. Long;Tianqing An
基于对辛群中奇异子集、其补子集和双曲子集的整体拓扑的理解，本文研究了双曲Hamilton系统的不稳定域，并定义了这类不稳定域的特征指数.这个指数是通过辛路径的Maslov型指数理论定义的，从C. Conley，E. Zehnder和Y.以及辛矩阵的双曲指数。变分法中的非退化局部极小与双曲极值环不稳定性之间的关系的老问题也研究了通过这个新的指标的不稳定域。
Based upon the understanding of the global topologies of the singular subset, its complement, and the hyperbolic subset in the symplectic group, in this paper we study the domains of instability for hyperbolic Hamiltonian systems and define a characteristic index for such domains. This index is defined via the Maslov-type index theory for symplectic paths starting from the identity defined by C. Conley, E. Zehnder, and Y. Long, and the hyperbolic index of symplectic matrices. The old problem of the relation between the non-degenerate local minimality and the instability of hyperbolic extremal loops in the calculus of variation is also studied via this new index for the domains of instability.