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Jacek Chądzyński, Tadeusz Krasiński (1992)
Annales Polonici Mathematici
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A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.
Ha Huy Vui, Nguyen Hong Duc (2008)
Annales Polonici Mathematici
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We give the formula expressing the Łojasiewicz exponent near the fibre of polynomial mappings in two variables in terms of the Puiseux expansions at infinity of the fibre.
Ewa Ligocka (2006)
Annales Polonici Mathematici
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We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.
Gianluca Gorni, Gaetano Zampieri (1996)
Annales Polonici Mathematici
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Ewa Ligocka (1998)
Colloquium Mathematicae
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R. Ger (1971)
Annales Polonici Mathematici
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Jason Lucier (2006)
Acta Arithmetica
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Umberto Zannier (2007)
Acta Arithmetica
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J. Achari (1978)
Matematički Vesnik
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G. Spiliopoulos (1991)
Fundamenta Mathematicae
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J. Siciak (1971)
Annales Polonici Mathematici
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Luís R. A. Finotti (2009)
Acta Arithmetica
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Norbert Hegyvári, François Hennecart (2009)
Acta Arithmetica
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Maciej Klimek (2003)
Annales Polonici Mathematici
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It is shown that an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively.
Ewa Ligocka (2009)
Annales Polonici Mathematici
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We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.
J. Bochnak, W. Kucharz (1990)
Annales Polonici Mathematici
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A. Schinzel (2008)
Acta Arithmetica
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I. Marinković (1977)
Matematički Vesnik
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W. Głocki (1987)
Applicationes Mathematicae
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