Index Theory for Symplectic Matrix Paths with Applications

作者: Yiming Long

DOI:

关键词:

摘要: In this lecture notes, I give an introduction on the Maslov-type index theory for symplectic matrix paths and its iteration with applications to existence, multiplicity, stability of periodic solution orbit problems nonlinear Hamiltonian systems closed geodesic manifolds, including a survey recent progresses in these areas.

参考文章(79)
Nancy Hingston, On the growth of the number of closed geodesics on the two-sphere International Mathematics Research Notices. ,vol. 1993, pp. 253- 262 ,(1993) , 10.1155/S1073792893000285
V. M. Starzhinskiĭ, V. A. I︠A︡kubovich, Linear differential equations with periodic coefficients Wiley , Israel Program for Scientific Translations. ,(1975)
A. I. Fet, Variational problems on closed manifolds American Mathematical Society. ,(1953)
Hans-Bert Rademacher, On the average indices of closed geodesics Journal of Differential Geometry. ,vol. 29, pp. 65- 83 ,(1989) , 10.4310/JDG/1214442633
Wilhelm Klingenberg, Lectures on closed geodesics ,(1978)
W. Ballmann, G. Thorbergsson, W. Ziller, Existence of closed geodesics on positively curved manifolds Journal of Differential Geometry. ,vol. 18, pp. 221- 252 ,(1983) , 10.4310/JDG/1214437662