A solution to the bidimensional global asymptotic stability conjecture

 Access to full text

 Full (PDF)

1. [1] M.A. Aizerman, On a problem concerning the stability in the large of dynamical systems., Uspehi Mat. Nauk. N. S., Vol. 4, (4), pp. 187-188. Zbl0040.19601MR31610
2. [2] N.E. Barabanov, On a problem of Kalman., Siberian Mathematical Journal, Vol. 29, (3), 1988, pp. 333-341. Zbl0713.93044MR953016
3. [3] R. Fessler, A solution of the two dimensional Global Asymptotic Jacobian Stability Conjecture, Preprint. ETH-Zentrum, Switzerland. Zbl0835.34052
4. [4] A. Gasull, J. Llibre and J. Sotomayor, Global asymptotic stability of differential equations in the plane, J. diff. Eq., 1989, To appear. Zbl0732.34045MR1111178
5. [5] A. Gasull and J. Sotomayor, On the basin of attraction of dissipative planar vector fields, Lecture Notes in Mathematics. Springer-Verlag. Procc. Coll. Periodic Orbits and Bifurcations. Luminy, 1989, To appear. Zbl0713.34053MR1094380
6. [6] G. Gorni and G. Zampieri, On the global conjecture for global asymptotic stability, 1990, To appear. Zbl0739.34047
7. [7] C. Gutierrez, Dissipative vector fields on the plane with infinitely many attracting hyperbolic singularities, Bol. Soc. Bras. Mat., Vol. 22, No. 2, 1992, pp. 179-190. Zbl0776.34024MR1179484
8. [8] P. Hartman, On stability in the large for systems of ordinary differential equations, Can. J. Math., Vol. 13, 1961, pp. 480-492. Zbl0103.05901MR123791
9. [9] P. Hartman, Ordinary differential equations, Sec. Ed. Birkhäuser, 1982. Zbl0476.34002MR658490
10. [10] R.E. Kalman, On Physical and Mathematical mechanisms of instability in nonlinear automatic control systems, Journal of Applied Mechanics Transactions, ASME, Vol. 79, (3), 1957, pp. 553-566. MR88420
11. [11] N.N. Krasovskii, Some problems of the stability theory of motion, 1959, In russian. Gosudartv Izdat. Fiz. Math. Lit., Moscow., English translation, Stanford University Press, 1963. 
12. [12] L. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Math. J., Vol. 12, 1960, pp. 305-317. Zbl0096.28802MR126019
13. [13] G. Meisters and O. Olech, Global Stability, injectivity and the Jacobian Conjecture, To appear in the Procc. of the First World Congress on Nonlinear Analysis held at Tampa, Florida. August, 1992. Zbl0854.34054
14. [14] G. Meisters and O. Olech, Solution of the global asymptotic stability Jacobian conjecture for the polynomial case, Analyse Mathématique et applications. Contributions en l'honneur de J. L. Lions., Gauthier-Villars, Paris, 1988, pp. 373-381. Zbl0668.34048MR956968
15. [15] C. Olech, On the global stability of an autonomous system on the plane, Cont. toDiff. Eq., Vol. 1, 1963, pp. 389-400. Zbl0136.08602MR147734
16. [16] B. Smith and F. Xavier, Injectivity of local diffeomorphisms from nearly spectral conditions, University of Notre Dame, Preprint, 1993.