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.

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.

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.

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.