Annali di Matematica Pura ed Applicata

, Volume 12, Issue 1, pp 117–133 | Cite as

On the periodic motions near a given periodic motion of a dynamical system

  • G. D. Birkhoff
  • D. C. LewisJr.


Dynamical System Periodic Motion 
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  1. (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
  2. (1).
    Cf.G. D. Birkhoff,Dynamical Systems, Chapter III, particularly § 9. Also Chapter VI, § 1.Google Scholar
  3. (1).
    Êmile Borel,Leçons sur la théorie de la croissance, p. 149.Google Scholar

Copyright information

© Nicola Zanichelli 1934

Authors and Affiliations

  • G. D. Birkhoff
    • 1
  • D. C. LewisJr.
    • 1
  1. 1.CambridgeU. S. A.

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