Monotonicity of the period map of a non-Hamiltonian center

• Autores: Jorge Billeke, Eduardo Sáez
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 45, Fasc. 2, 1994, págs. 177-182
• Idioma: inglés
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• Resumen

  • In this paper we prove that the period map of $$\ddot{x}- ax\thinspace\dot{x} + x^3 = 0,\quad with\quad a^2 < 8 ,$$ is monotonically decreasing. As an application, it is obtained that the respective Dirichlet boundary problem for two points has either a unique solution or no solution at all while the Neumann boundary value problem has a unique solution.

• Referencias bibliográficas
  • C. Chicone, The Monotonicity of the Period Function for Planar Hamiltonian Vector Fields. Journal of Differential Equations, 69 (1987), 310–321.
  • S. N. Chow and J. A. Sanders, On the Number of Critical Points of the Period. Journal of Differential Equations, 64 (1986), 51–66.
  • C. Chicone and F. Dumortier, Finiteness of Critical Periods of Planar Analytic Vector Fields. Preprint Department of Mathematics University...
  • C. Chicone and M. Jacobs, Bifurcations of Critical Periods for Plane Vector Fields. Transactions of the American Mathematical Society. Volume...
  • L. Gavrilov, Remark on the Number of Critical Points of the Period. Journal of Differential Equations, 101 (1993), 58–65.
  • R. E. Kooij and P. G. Barkker, Three-dimensional viscous flow structures from bifurcation of a degenerate singularity with three zeros eigenvalues....
  • A. Lyapunov, Problème général de la stabilité du mouvement. Annals of Math Studies, 17 Princeton University Press. Princeton, 1949.