DOI QR코드

DOI QR Code

NOTE ABOUT THE ISOCHRONICITY OF HAMILTONIAN SYSTEMS AND THE CURVATURE OF THE ENERGY

  • Gomez, Blas Herrera
  • Published : 2007.08.31

Abstract

In this note we show the relationship between the period of a isochronous center of a planar Hamiltonian system and the Gauss curvature of the surface S = (x, y, H(x, y)) where H is the energy function of the system.

Keywords

Hamiltonian systems;Gauss curvature;isochronous center

References

  1. A. Cima, F. Manosas, and J. Villadelprat, Isochronicity for Several Classes of Hamilton- ian Systems, J. Differential Equations 157 (1999), no. 2, 373-413 https://doi.org/10.1006/jdeq.1999.3635
  2. H. Ito, Convergence of Birkhoff Normal Forms for Integrable Systems, Comment. Math. Helv. 64 (1989), no. 3, 412-461 https://doi.org/10.1007/BF02564686
  3. J. Villadelprat, Index of Vector Fields on Manifolds and Isochronicity for Planar Hamiltonian Differential Systems, Ph. D. Thesis, Pub. Univ. Autonoma de Barcelona, 1999