Skip to main content
SpringerLink
Log in

On the convergence of normalizations of real analytic surfaces near hyperbolic complex tangents

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bedford, E., Levi flat hypersurfaces in ℂ2 with prescribed boundary, Ann. Scuola Norm. Sup. di Pisa9 (1982), 529–570.

    MathSciNet  Google Scholar 

  2. Birkhoff, G. D.,Surface transformations and their dynamical applications, Acta Math.43 (1920), 1–119.

    Article  Google Scholar 

  3. Bishop, E.,Differentiable manifolds in complex Euclidean space, Duke Math. J.32 (1965), 1–22.

    Article  MathSciNet  Google Scholar 

  4. Dulac, H.,Recherches sur les points singuliers des équations différentielles, J. de L’Ecole Poly., série 2,9 (1904), 1–125.

    Google Scholar 

  5. Gong, X.,Thesis, University of Chicago, Chicago, August, 1974.

  6. Ito, H.,Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv.64 (1989), 412–461.

    Article  MathSciNet  Google Scholar 

  7. Klingenberg, W., Asymptotic curves on real analytic surfaces in ℂ2, Math. Ann.273 (1985), 149–162.

    Article  MathSciNet  Google Scholar 

  8. Moser, J. K., Analytic surfaces in ℂ2 and their local hull of holomorphy, Ann. Acad. Sci. Fenn. Ser. A. I. Math.10 (1985), 397–410.

    MathSciNet  Google Scholar 

  9. Moser, J. K. andWebster, S. M., Normal forms for real surfaces in ℂ2 near complex tangents and hyperbolic surface transformations, Acta Math.150 (1983), 255–296.

    Article  MathSciNet  Google Scholar 

  10. Pliss, V. A.,On the reduction of an analytic system of differential equations to linear form, Diff. Equation1 (1965), 111–118.

    Google Scholar 

  11. Rüssmann, H.,Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Näche einer Gleichgewichtslösung, Math. Ann.169 (1967), 55–72.

    Article  MathSciNet  Google Scholar 

  12. Siegel, C. L.,On integrals of canonical systems, Ann. Math.42 (1941), 806–822.

    Article  Google Scholar 

  13. Siegel, C. L.,Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Ann.128 (1954), 144–170.

    Article  MathSciNet  Google Scholar 

  14. Vey, J.,Sur certains systèmes dynamiques séperables, Amer. J. Math.100 (1978), 591–614.

    Article  MathSciNet  Google Scholar 

  15. Webster, S. M., The Euler and Pontrijagin numbers of an n-manifold in ℂ2, Comment. Math. Helv.60 (1985), no. 2, 193–216.

    MathSciNet  Google Scholar 

  16. Webster, S. M.,Holomorphic symplectic normalization of a real function, Ann. Scuola Norm. Sup. di Pisa19 (1992), 69–86.

    MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. Xianghong Gong

    Present address: Institute for Advanced Study, School of Mathematics, 08540, Princeton, NJ, USA

Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA

    Xianghong Gong

Authors
  1. Xianghong Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gong, X. On the convergence of normalizations of real analytic surfaces near hyperbolic complex tangents. Commentarii Mathematici Helvetici 69, 549–574 (1994). https://doi.org/10.1007/BF02564504

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564504

Keywords

Search

Navigation