Hoelder continuity property of composite Julia sets

• Autorzy: Kosek M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the composite Julia associated with a finite family of the proper polynomial mappings in [C^n]. We show its pluricomplex Green function is Hoelder continous. This yields in particular that the set preserves Markov's inequality.

Słowa kluczowe

EN

analytic spaces; complex dynamics; extremal plurisubharmonic functions; geometric convexity; partial differential operators; potential theory; several complex variables

PL

funkcje plurisubharmoniczne; funkcje wielu zmiennych zespolonych; przestrzenie analityczne; teoria potencjału; wypukłość geometryczna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 4
• Strony: 391--399
• Opis fizyczny: Bibliogr. 21 poz.,

Twórcy

autor

Kosek M.

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków

Bibliografia

• [1] W. Pleśniak, Recent progres in multavariate Markov inequality, in: Approximation Theory, Special Volume in Меmorу of Pтofessor Varma, eds.: N. K. Govil, J. Szabados, Marcel Dekker Inc., New York 1997.
• [2] J. Siciak, Extremal plurisubharmonic functions in Сn, Ann. Polon. Math., 39 (1981) 175-211.
• [3] J. Siciak, On metrics associated with extremal plurisubharmonic functions, Bul. Po1. Ac.: Math., 45(2) (1997) 151-161.
• [4] L. Garleson, T. W. Gamelin, Complex Dynamics, Springer, New York 1993.
• [5] L. Baribeаu, T. J. Ransford, Meromorphic imultifunctions in complex dуnаmics, Ergodic Theory Dynamical Systems, 12 (1992) 39-52.
• [6] Ј. E. Fornaess, N. Sibonу, Complex dynamics in higher dimension I, Astérisque, 222 (1994) 201-231.
• [7] М. Klimek, Metrics associated with extremal plurisubharmonic func,ions, Proc. Amer. Math. Soc., 123(9) (1995) 2763-2770.
• [8] М. Klimek, Inverse iteration systems in Сn, Acta Universitatis Upsaliensis, to be published.
• [9] М. Kosek; Hölder Continuity Property of filled-in Julia sets in Сn, Proc. Amer. Math. Soc., 125(7) (1997) 2029-2032.
• [10] Ј. E. Fornaess, N. Sibony, Complex Hénon mappings in Cn and Fatou-Bieberliach domains, Duke Math. Journal, 65 (1992) 345-380.
• [11] S. Friedland; J. Milner, Dynаmical properties of plane polynomial automorphisms, Ergodic Theory Dynamical Systems, 9 (1989) 67-99.
• [12] М. Klimek, Pluripocential Тhеоrу, Oxford University Press, Oxford-New York-Tokyo 1991.
• [13] C. Kuratowski, Topologie Vol. II, PWN, Warszawa 1961.
• [14] D. H. Armitage, U. Kuran, The convexity of a domain and the subharmonicity of the signed distance function, Proc. Amer. Math. Soc., 93 (1985) 598-600.
• [15] J. Siciak, Wiener's type sufficient conditions in CN, Univ. Iagl. Acta Math., 35 (1997) 47-74.
• [16] A. A. Мarkov, On а problem posed by D. I. Mendeleev (in Russian), Izv. Akad. Nauk. St-Petersbourg, 62 (1889) 1-24.
• [17] J. Siciak, Deqree of convergence of some sequences in the conformal mnapping theory, Colloq. Math., 16 (1967) 49-59.
• [18] J. Lithneг, Comparing two versions of Markov's inequality on compact sets, J. Approx. Theory, 77 (1994) 202-211.
• [19] L. Вiałas-Cież, Equivalence of Markov's propеrty and Hölder continuity of the. Green function for Cantor-type sets, East Journal on Approximations, 1(2) (1995) 249-253.
• [20] L. Вiałas-Cież, Markov sets in C are not pluripolar, Bull. Pоl. Ac.: Math., 46(1) (1998) 83-89.
• [21] A. Płoski, On the growth of proper polynomial mappings, Annn. Polon. Math., 45 (1985) 297-309.