A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS

数学物理学报(英文版) ›› 1997, Vol. 17 ›› Issue (3): 301-308.

A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS

古志鸣

Nanjing University of Aeronautics and A stronautics, Nanjing 210016, China

收稿日期:1995-10-19 修回日期:1996-05-30 出版日期:1997-09-25 发布日期:1997-09-25

A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS

Gu Zhiming

Nanjing University of Aeronautics and A stronautics, Nanjing 210016, China

Received:1995-10-19 Revised:1996-05-30 Online:1997-09-25 Published:1997-09-25

摘要/Abstract

摘要： A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question:How many types of the periodic small oscillation ill the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by tile Betti numbers and dimension of the constraint manifold only.

关键词: large-scale estimate, periodic motion, Morse theory

Abstract: A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question:How many types of the periodic small oscillation ill the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by tile Betti numbers and dimension of the constraint manifold only.

Key words: large-scale estimate, periodic motion, Morse theory

古志鸣. A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS[J]. 数学物理学报(英文版), 1997, 17(3): 301-308.

Gu Zhiming. A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS[J]. Acta mathematica scientia,Series B, 1997, 17(3): 301-308.

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A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS

A LARGE-SCALE ESTIMATE OF THE NUMBER OF PERIODIC SMALL OSCILLATIONS OF NONLINEAR SYSTEMS

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