Displaying similar documents to “The Jacobian Conjecture: survey of some results”

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.

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 counterexample to a conjecture of Drużkowski and Rusek

Arno van den Essen (1995)

Annales Polonici Mathematici

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Let F = X + H be a cubic homogeneous polynomial automorphism from n to n . Let p be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that d e g F - 1 3 p - 1 . We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.

A finite dimensional reduction of the Schauder Conjecture

Espedito De Pascale (1993)

Commentationes Mathematicae Universitatis Carolinae

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Schauder’s Conjecture (i.eėvery compact convex set in a Hausdorff topological vector space has the f.p.p.) is reduced to the search for fixed points of suitable multivalued maps in finite dimensional spaces.

A consequence of an effective form of the abc-conjecture

Jerzy Browkin (1999)

Colloquium Mathematicae

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T. Cochrane and R. E. Dressler [CD] proved that the abc-conjecture implies that, for every > 0, the gap between two consecutive numbers A A 0 . 4 with two exceptions given in Table 2.

Basic properties of shift radix systems.

Akiyama, Shigeki, Borbély, Tibor, Brunotte, Horst, Pethő, Attila, Thuswaldner, Jörg M. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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