A geometry of Pinchuk's map

• Autorzy: Goździewicz, G.
• Języki publikacji: EN

Abstrakty

EN

Sergey Pinchuk found a polynomial map from the real plane to itself which is a local diffeomorphism but is not one-to-one. The aim of this paper is to give a geometric description of Pinchuk's map.

Słowa kluczowe

PL

geometria algebraiczna; odwzorowanie wielomianu rzeczywistego

EN

Jacobian Conjecture; real polynomial mappings

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 1
• Strony: 69--75
• Opis fizyczny: Bibliogr. 8 poz.,

Twórcy

autor

Goździewicz, G.

• Kielce University 0f Technology, Al, Tysiąclecia Państwa Polskiego 7, 25-314, Kielce, Poland,

Bibliografia

• [1] R. Benedetti, J.-J. Risler, Real algebraic and semi-algebraic sets, Hermann, Paris 1990.
• [2] L. A. Campbell, Picturing Pinchuk's plane polynomial pair, preprint math. AG/9812032.
• [3] Z. Jelonek, A geometry of polynomial transformations of the real plane, Bull. Pol. Ac.: Math., this issue, 59-62.
• [4] Z. Jelonek, The set of points at which a polynomial map is not proper, Ann. Polon. Math., 58 (1993) 259-266.
• [5] Z. Jelonek, Geometry of abine polynomial mappings, preprint PAN, 1997/570.
• [6] A. Parusiński, Z. Szafraniec, On the Euler characteristic of fibres of real polynomial maps, Singularities Symposium Łojasiewicz 70, Banach Center Publ., 44 (1998) 175-182.
• [7] R. Peretz, The variety of the asymptotiv values of a real polynomial etale map, J. Pure Appl. Algebra, 106 (1996) 103-112.
• [8] S. Pinchuk, A Counterexample to the Real Jacobian Conjecture, Math. Z., 217 (1994) 1-4.