The degree of the inverse of a polynomial automorphism.

Brusadin, Sabrina; Gorni, Gianluca

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Displaying similar documents to “The degree of the inverse of a polynomial automorphism.”

Jung's type theorem for polynomial transformations of ℂ²

Sławomir Kołodziej (1991)

Annales Polonici Mathematici

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We prove that among counterexamples to the Jacobian Conjecture, if there are any, we can find one of lowest degree, the coordinates of which have the form $x^{m} y^{n}$ + terms of degree < m+n.

Growth at infinity of a polynomial with a compact zero set

Janusz Gwoździewicz (1998)

Banach Center Publications

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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.

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

Ayad, Ali (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

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

Yuri Bilu, Robert Tichy (2000)

Acta Arithmetica

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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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Resultant and the Łojasiewicz exponent

J. Chądzyński, T. Krasiński (1995)

Annales Polonici Mathematici

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An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.

Wold decomposition of the Hardy space and Blaschke products similar to a contraction

M. Stessin (1999)

Colloquium Mathematicae

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The classical Wold decomposition theorem applied to the multiplication by an inner function leads to a special decomposition of the Hardy space. In this paper we obtain norm estimates for componentwise projections associated with this decomposition. An application to operators similar to a contraction is given.

Characterization of smooth, compact algebraic curves in ℝ²

L. Bos, N. Levenberg, B. Taylor (1995)

Banach Center Publications

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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.