Jung's type theorem for polynomial transformations of ℂ²

Sławomir Kołodziej

Displaying similar documents to “Jung's type theorem for polynomial transformations of ℂ²”

The degree of the inverse of a polynomial automorphism.

Brusadin, Sabrina, Gorni, Gianluca (2006)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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A geometric approach to the Jacobian Conjecture in ℂ²

Ludwik M. Drużkowski (1991)

Annales Polonici Mathematici

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We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set $g^{- 1} (0)$ (resp. $f^{- 1} (0)$ ), then (f,g) is bijective.

Formulae for the singularities at infinity of plane algebraic curves.

Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Growth at infinity of a polynomial with a compact zero set

Janusz Gwoździewicz (1998)

Banach Center Publications

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Puiseux series solutions of ordinary polynomial differential equations: complexity study.

Ayad, Ali (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

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Non-zero constant Jacobian polynomial maps of $ℂ ²$

Nguyen Van Chau (1999)

Annales Polonici Mathematici

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We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.

Extension of polynomial mappings with a given Łojasiewicz exponent.

Karaś, Marek (2007)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Salomon's Theorem for polynomials with several parameters

Maria Frontczak, Przemysław Skibiński, Stanisław Spodzieja (1999)

Colloquium Mathematicae

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The Diophantine equation f(x) = g(y)

Yuri Bilu, Robert Tichy (2000)

Acta Arithmetica

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Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

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Thomas’ conjecture is, given monic polynomials $p_{1},$ $..., p_{d} \in ℤ [a]$ with $0 < deg p_{1} < \dots < deg p_{d}$ , then the Thue equation (over the rational integers) $(X - p_{1} (a) Y) \dots (X - p_{d} (a) Y) + Y^{d} = 1$ has only trivial solutions, provided $a \geq a_{0}$ with effective computable $a_{0}$ . We consider a function field analogue of Thomas’ conjecture in case of degree $d = 3$ . Moreover we find a counterexample to Thomas’ conjecture for $d = 3$ .

Approximation exponents for algebraic functions in positive characteristic

Bernard de Mathan (1992)

Acta Arithmetica

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In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type $α = (A α^{q} + B) / (C α^{q} + D)$ , where q is a power of p.