Article PDF
Literatur
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.
Cf.G. D. Birkhoff,Dynamical Systems, Chapter III, particularly § 9. Also Chapter VI, § 1.
Êmile Borel,Leçons sur la théorie de la croissance, p. 149.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Birkhoff, G.D., Lewis, D.C. On the periodic motions near a given periodic motion of a dynamical system. Annali di Matematica 12, 117–133 (1934). https://doi.org/10.1007/BF02413852
Issue Date:
DOI: https://doi.org/10.1007/BF02413852