Janusz Gwoździewicz, Maciej Sękalski (2004)
Annales Polonici Mathematici
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We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.
Zheng, Bo, Xiao, Huafeng, Shi, Haiping (2011)
Boundary Value Problems [electronic only]
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Adam Epstein, Thomas Sharland (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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We give a Thurston classification of those bicritical rational maps which have two period two superattracting cycles. We also show that all such maps are constructed by the mating of two unicritical degree polynomials.
Perera, Kanishka (1998)
Abstract and Applied Analysis
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Perera, Kanishka (1998)
Abstract and Applied Analysis
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A. Bahri (1986-1987)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Li, Shujie, Su, Jiabao (1996)
Abstract and Applied Analysis
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Denis Bonheure, Miguel Ramos (2009)
Annales de l'I.H.P. Analyse non linéaire
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Yahya Ould Hamidoune, Oriol Serra, Gilles Zémor (2006)
Acta Arithmetica
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Janusz Gwoździewicz, Stanisław Spodzieja (2005)
Annales Polonici Mathematici
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Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
Joan C. Artés, Jaume Llibre (1997)
Publicacions Matemàtiques
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We study phase portraits of quadratic vector fields with a weak focus of third order at the origin. We show numerically the existence of at least 20 different global phase portraits for such vector fields coming from exactly 16 different local phase portraits available for these vector fields. Among these 20 phase portraits, 17 have no limit cycles and three have at least one limit cycle.