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Dynamics of Quasi-parabolic One-Resonant Biholomorphisms

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Abstract

In this paper we study the dynamics of germs of quasi-parabolic one-resonant biholomorphisms of ℂn+1 fixing the origin, namely, those germs whose differential at the origin has one eigenvalue 1 and the others having a one-dimensional family of resonant relations. We define some invariants and give conditions which ensure the existence of attracting domains for such maps.

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Acknowledgements

We thank the referee for his/her comments which improved the original manuscript.

Part of this work was done while the second named author was visiting IHÉS and Dipartimento di Matematica, Università di Roma “Tor Vergata”. He would like to thank the hosts for their hospitality and the institutes and K.C. Wong Education Foundation for the support.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    Filippo Bracci

  2. Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, P.R. China

    Feng Rong

Authors
  1. Filippo Bracci
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  2. Feng Rong
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Corresponding author

Correspondence to Feng Rong.

Additional information

Communicated by Marco Abate.

F. Bracci is partially supported by the ERC grant “HEVO—Holomorphic Evolution Equations” No. 277691.

F. Rong is partially supported by the National Natural Science Foundation of China (Grant No. 11001172), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100073120067), and the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars.

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Bracci, F., Rong, F. Dynamics of Quasi-parabolic One-Resonant Biholomorphisms. J Geom Anal 24, 1497–1508 (2014). https://doi.org/10.1007/s12220-012-9382-5

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  • DOI: https://doi.org/10.1007/s12220-012-9382-5

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