Geometric Scattering Monodromy

• Richard Cushman ^[1]
  1. [1] University of Calgary

     University of Calgary

     Canadá

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper we give geometric conditions so that the integral mapping of a Liouville integrable Hamiltonian system with a focus-focus equilibrium point has scattering monodromy. Using a complex version of the Morse lemma, we show that scattering monodromy is the same as the scattering monodromy of the standard focus-focus system.

• Referencias bibliográficas
  • 1. Bates, L., Cushman, R.: Scattering monodromy and the A1 singularity. Cent. Eur. J. Math. 5, 429–451 (2007)
  • 2. Cushman, R.H., Bates, L.M.: Global aspects of classical integrable systems, 2nd edn. Birkhäuser, Basel (2015)
  • 3. Dullin, H.R., Waalkens, H.: Nonuniqueness of the phase shift in central scattering due to monodromy. Phys. Rev. Lett. 101, 070405 (2008)
  • 4. Efstathiou, K., Giacobbe, A., Marde˘si´c, P.: Rotation forms and local monodromy. J. Math. Phys 58, 022902 (2017)
  • 5. Martynchuk, N., Broer, H.W., Efstathiou, K.: Hamiltonian monodromy and Morse theory. Comm. Math. Phys. 375, 1373–1392 (2020)
  • 6. Vu Ngoc, S., Wacheux, C.: Smooth normal forms for integrable Hamiltonian systems near a focus-focus singularity. Acta. Math. Vietnam 38,...