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The Best Bound on the Rotations in the Stability of Periodic Solutions of a Newtonian Equation
Author(s) -
Zhang Meirong
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003939
Subject(s) - twist , linearization , mathematics , newtonian fluid , mathematical analysis , third order , stability (learning theory) , upper and lower bounds , scalar (mathematics) , lyapunov function , classical mechanics , physics , geometry , nonlinear system , computer science , philosophy , theology , quantum mechanics , machine learning
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 isθ 0 * = arccos ( − 1 / 4 ) . .
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