On the periodic motions near a given periodic motion of a dynamical system
KeywordsDynamical System Periodic Motion
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- (1).A critical point is a point for whichdJ=0; these are to be counted with their proper multiplicity. The existence of two critical points — maximum and minimum — is obvious. An easy method of establishing the existence of 2n – 2 other critical points is to applyM. Morse's critical point relations (see, for instance, his paper,Relations between the Critical Points of a Real Function of nReal Variables, « Trans. Am. Math. Soc. », vol. 27 (1925), pp. 345–356) to then dimensional torus for which the connectivity numbers (mod 2) are the binomial coefficients.Google Scholar
- (1).Cf.G. D. Birkhoff,Dynamical Systems, Chapter III, particularly § 9. Also Chapter VI, § 1.Google Scholar
- (1).Êmile Borel,Leçons sur la théorie de la croissance, p. 149.Google Scholar
© Nicola Zanichelli 1934