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Journal of the London Mathematical Society 2003 67(1):137-148; doi:10.1112/S0024610702003939
© 2003 by London Mathematical Society
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© The London Mathematical Society

The Best Bound on the Rotations in the Stability of Periodic Solutions of a Newtonian Equation

Meirong Zhang

Department of Mathematical Sciences, Tsinghua University Beijing 100084, China, mzhang{at}math.tsinghua.edu.cn

Received 18 September 2001. Revision received 22 March 2002.

In most cases, the third order approximation of a scalar Newtonian equation can lead to the Lyapunov stability of a periodic solution through the obtaining of a nonzero twist coefficient. Recently, Ortega obtained the twist property of a periodic solution when the second order coefficient does not change sign and the third one is negative under a crucial limitation to the rotation of the linearization equation. The paper finds that the best bound on the limitation of the rotations is Formula.


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