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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The iteration formula
of the Maslov-type index theory
with applications
to nonlinear Hamiltonian systems


Authors: Di Dong and Yiming Long
Journal: Trans. Amer. Math. Soc. 349 (1997), 2619-2661
MSC (1991): Primary 58F05, 58E05, 34C25; Secondary 15A18, 15A21
DOI: https://doi.org/10.1090/S0002-9947-97-01718-2
MathSciNet review: 1373632
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous, periodic, and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems, and unify known results under various convexity conditions.


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Additional Information

Di Dong
Affiliation: Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Address at time of publication: Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3651
Email: ddong@math.sunysb.edu

Yiming Long
Affiliation: Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: longym@sun.nankai.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-97-01718-2
Keywords: Normal form of a symplectic matrix, perturbation of eigenvalues, symplectic path, Maslov-type index, iteration formula, minimal period, Hamiltonian systems
Received by editor(s): May 3, 1994
Additional Notes: The second author was partially supported by YTF of Edu. Comm., NNSF of China, and Qiu Shi Sci. and Tech. Foundations.
Article copyright: © Copyright 1997 American Mathematical Society