A note on the divergence-free Jacobian Conjecture in R2

• Autorzy: Sabatini M.
• Języki publikacji: EN

Abstrakty

EN

We give a shorter proof to a recent result by Neuberger [Rocky Mountain J. Math. 36 (2006)], in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results of Neuberger's paper.

Słowa kluczowe

EN

Jacobian Conjecture; divergence-free

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 2
• Strony: 109--115
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Sabatini M.

• Departimento di Matematica, Universita di Trento, 1-38050 Povo (TN), Italy,

Bibliografia

• [1] H. Bass, E. H. Connell and D. Wright, The Jacobian conjecture: reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. 7 (1982), 287-330.
• [2] M. de Bondt and A. van den Essen, Recent progress on the Jacobian Conjecture, Bull. Amer. Math. Soc. 7 (1982), 287-330.
• [3] A. Cima, A. van den Essen, A. Gasull, E. Rubbers and F. Manyosas, A polynomial counter-example to the Markus-Yamabe conjecture, Adv. Math. 131 (1997), 453-457.
• [4] L. Drużkowski, An effective approach to Keller’s Jacobian conjecture, Math. Ann. 264 (1983), 303-313.
• [5] R. Fessler, A proof of the two-dimensional Markus-Yamabe stability conjecture and a generalization, Ann. Polon. Math. 62 (1995), 45-74.
• [6] A. A. Glutsyuk, Complete solution of the Jacobian problem for planar vector fields, Uspekhi Mat. Nauk 49 (1994), no. 3, 179-180 (in Russian); English transl.: Russian Math. Surveys 49 (1994), 185-186.
• [7] C. Gutierrez, A solution to the bidimensional global asymptotic stability conjecture, Ann. Inst. H. Poincare Anal. Non Lineaire 12 (1995), 627-671.
• [8] O. H. Keller, Ganze Cremona-Transformationen, Monatsh. Math. Phys, 47 (1939), 299-306.
• [9] G. Meisters, Jacobian problems in differential equations and algebraic geometry, Rocky Mountain J. Math. 12 (1982), 679-705.
• [10] L. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Math. J. 12 (1960), 305-317.
• [11] J. W. Neuberger, The divergence-free Jacobian conjecture in dimension two, Rocky Mountain J. Math. 36 (2006), 265-271.
• [12] C. Olech, On the global stability of an autonomous system in the plane, Contributions to Differential Equations 1 (1963), 389-400.