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THE BEST BOUND ON THE ROTATIONS IN THE STABILITY OF PERIODIC SOLUTIONS OF A NEWTONIAN EQUATION

Published online by Cambridge University Press:  25 March 2003

MEIRONG ZHANG
MEIRONG ZHANG
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, Chinamzhang@math.tsinghua.edu.cn
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Abstract

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 $\theta^*_0=\arccos(-1/4)$.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 137 - 148
Copyright
The London Mathematical Society, 2003

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