On the periodic motions near a given periodic motion of a dynamical system
Author:
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics
Link
http://link.springer.com/content/pdf/10.1007/BF02413852.pdf
Reference3 articles.
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 2 n – 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.
2. Cf.G. D. Birkhoff,Dynamical Systems, Chapter III, particularly § 9. Also Chapter VI, § 1.
3. Êmile Borel,Leçons sur la théorie de la croissance, p. 149.
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