대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제44권3호
  • /
  • Pages.415-418
  • /
  • 2007
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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NOTE ABOUT THE ISOCHRONICITY OF HAMILTONIAN SYSTEMS AND THE CURVATURE OF THE ENERGY

  • Gomez, Blas Herrera (DEPARTMENT D'ENGINYERIA INFORMATICA I MATEMATIQUES UNIVERSITAT ROVIRA I VIRGILI)
  • 발행 : 2007.08.31
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초록

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.

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참고문헌

  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