Iteration inequalities of the Maslov-type index theory with applications

Liu CG.; Long YM.

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Iteration inequalities of the Maslov-type index theory with applications

机译：Maslov型指数理论的迭代不等式及其应用

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In this paper, by using the omega-index theory introduced by Y. Long in (1999, Pacific J. 1Math. 187, 113-149), in particular, the splitting numbers, Maslov-type mean index, and the homotopy component of symplectic matrix, we establish various inequalities of the Maslov-type index theory for iterations of symplectic paths starting from the identity. As an application, these results are used to study Rabinowitz' conjecture on the prescribed minimal period solution problem of nonlinear Hamiltonian systems. (C) 2000 Academic Press. [References: 32]

机译：本文使用Y. Long在（1999，Pacific J. 1Math。187，113-149）中引入的欧米伽指数理论，特别是分裂数，Maslov型均值指数和辛矩阵，我们建立了Maslov型指数理论的各种不等式，用于从恒等式开始的辛路径迭代。作为应用，这些结果用于研究非线性哈密顿系统的规定最小周期解问题上的拉比诺维茨猜想。（C）2000学术出版社。 [参考：32]

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《Journal of Differential Equations》 |2000年第2期|共22页
作者
Liu CG.; Long YM.;
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正文语种 eng
中图分类数学;
关键词
Maslov-type index; Iteration inequality; Hamiltonian system; Prescribed minimal period solution; Nonlinear hamiltonian-systems; Minimal period problem; Hypersurfaces; Formula;

机译：Maslov型指数;迭代不等式;哈密顿系统;规定的最小周期解;非线性哈密顿系统;最小周期问题;超曲面;公式;

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3. Matrix inequalities with applications to the theory of iterated kernels [J] . Banks W., Harcharras A., Neuwirth S., Linear Algebra and its Applications . 2003,第0期

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4. Session-Workshop on Analysis, Inequalities andHomogenization Theory and Applications [C] . Lars-Erik Persson, Natasha Samko International Conference on Numerical Analysis and Applied Mathematics . 2010

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5. Iterative path integral stochastic optimal control: Theory and applications to motor control. [D] . Theodorou, Evangelos A. 2011

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7. Iteration Inequalities of the Maslov-Type Index Theory with Applications [O] . Liu Chun-gen, Long Yiming 2000

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8. Iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems [R] . Di, D. , Yiming, L. 1994

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Iteration inequalities of the Maslov-type index theory with applications

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