Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

IMPACT FACTOR 2018: 0.726
5-year IMPACT FACTOR: 0.869

CiteScore 2018: 0.90

SCImago Journal Rank (SJR) 2018: 0.323
Source Normalized Impact per Paper (SNIP) 2018: 0.821

Mathematical Citation Quotient (MCQ) 2018: 0.34

ICV 2018: 152.31

Open Access
See all formats and pricing
More options …
Volume 3, Issue 3


Volume 13 (2015)

On regular polynomial endomorphisms of ℂ2 without bounded critical orbitswithout bounded critical orbits

Małgorzata Stawiska
Published Online: 2005-09-01 | DOI: https://doi.org/10.2478/BF02475914


We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints.

Keywords: Regular polynomial maps; hyperbolic invariant sets; external rays; landing

Keywords: 32H50; 37F15; 34M45

  • [1] E. Bedford and M. Jonsson: “Dynamics of regular polynomial endomorphisms of ℂk ”, Amer. J. Math., Vol. 122, (2000), pp. 153–212. CrossrefGoogle Scholar

  • [2] E. Bedford and M. Jonsson: “Potential theory in complex dynamics: regular polynomial mappings of ℂk ”, In: Complex analysis and geometry (Paris 1997), Progr. Math. Vol. 188, Birkhäuser, Basel, 2000, pp. 203–211. Google Scholar

  • [3] J.-Y. Briend and J. Duval: “Exposants de Liapounoff et distribution des points périodiques d'un endomorphisme de ℂℙk ”, Acta Math., Vol. 182(2), (1999), pp. 143–157. http://dx.doi.org/10.1007/BF02392572CrossrefGoogle Scholar

  • [4] A. Candel: “Uniformization of surface laminations”, Ann. Scient. Éc. Norm. Sup., Seria 4, Vol. 26, (1993), pp. 489–516. Google Scholar

  • [5] A. Douady and J.H. Hubbard: “Étude dynamique des polynomes complexes I”, Publ. Math. Orsay, (1984). Google Scholar

  • [6] J.E. Fornaess and N. Sibony: “Complex dynamics in higher dimension. Notes partially written by Estela A. Gavosto”, In: NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 439, Complex Potential Theory (Montreal, PQ, 1993), Kluwer Acad. Publ., Dordrecht, 1994, pp. 131–186. Google Scholar

  • [7] J.E. Fornaess and N. Sibony: “Oka's inequality for currents and applications”, Math. Ann., Vol. 301, (1998), pp. 339–419. Google Scholar

  • [8] J.E. Fornaess and N. Sibony: “Dynamics of ℙ2 (Examples)”, In: Laminations and foliations in dynamics, geometry and topology, Contemporary Mathematics 269, AMS, 2001, pp. 47–87. Google Scholar

  • [9] S. Heinemann: “Julia sets for endomorphisms of ℂn ”, Ergod. Th. & Dynam. Sys., Vol. 16, (1996), pp. 1275–1295. Google Scholar

  • [10] J.H. Hubbard and P. Papadopol: “Superattractive fixed points in ℂn ”, Indiana Univ. Math. J., Vol. 43(1), (1994), pp. 321–365. http://dx.doi.org/10.1512/iumj.1994.43.43014CrossrefGoogle Scholar

  • [11] S.L. Hruska: “Constructing an expanding metrics for the dynamical systems in one complex variable”, Nonlinearity, Vol. 18(1), (2005), pp. 81–100. http://dx.doi.org/10.1088/0951-7715/18/1/005CrossrefGoogle Scholar

  • [12] M. Klimek: “Metrics associated with extremal plurisubharmonic functions”, Proc. Amer. Math. Soc., Vol. 123(9), (1995), pp. 2763–2770. http://dx.doi.org/10.2307/2160572CrossrefGoogle Scholar

  • [13] S. Lang: Introduction to complex hyperbolic spaces, Springer-Verlag, New York, 1987. Google Scholar

  • [14] S. Łojasiewicz: “Sur les trajectoires du gradient d'une fonction analytique”, Univ. Stud. Bologna, (1983), pp. 115–117. Google Scholar

  • [15] S. Łojasiewicz: Introduction to complex analytic geometry, Translated from the Polish by Maciej Klimek, Birkhäuser Verlag, Basel, 1991. Google Scholar

  • [16] J. Milnor: Dynamics in one complex variable. Introductory lectures, Friedr. Vieweg & Sohn, Braunschweig, 1999. Google Scholar

  • [17] D. Ruelle: “Repellers for real analytic maps”, Ergod. Th. & Dynam. Sys., Vol. 2, (1982), pp. 99–107. http://dx.doi.org/10.1017/S0143385700009603CrossrefGoogle Scholar

  • [18] N. Sibony: “Dynamique des applications rationnelles de ℙk ”, In: Dynamique et géométrie complexes, Panoramas et Syntheses, Vol. 8, SMF, 1999, pp. 97–185. Google Scholar

  • [19] M. Stawiska: Repellers for regular polynomial endomorphisms of ℂk Thesis (PhD), Northwestern University, 2001. Google Scholar

  • [20] T. Ueda: “Critical orbits of holomorphic maps on projective spaces”, J. Geom. Anal., Vol. 8(2), (1998), pp. 319–334. Google Scholar

About the article

Published Online: 2005-09-01

Published in Print: 2005-09-01

Citation Information: Open Mathematics, Volume 3, Issue 3, Pages 398–403, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475914.

Export Citation

© 2005 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in