A solution to the bidimensional global asymptotic stability conjecture
Gutierrez, Carlos
Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995), p. 627-671 / Harvested from Numdam
Publié le : 1995-01-01
@article{AIHPC_1995__12_6_627_0,
     author = {Gutierrez, Carlos},
     title = {A solution to the bidimensional global asymptotic stability conjecture},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {12},
     year = {1995},
     pages = {627-671},
     mrnumber = {1360540},
     zbl = {0837.34057},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1995__12_6_627_0}
}
Gutierrez, Carlos. A solution to the bidimensional global asymptotic stability conjecture. Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) pp. 627-671. http://gdmltest.u-ga.fr/item/AIHPC_1995__12_6_627_0/

[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. | MR 31610 | Zbl 0040.19601

[2] N.E. Barabanov, On a problem of Kalman., Siberian Mathematical Journal, Vol. 29, (3), 1988, pp. 333-341. | MR 953016 | Zbl 0713.93044

[3] R. Fessler, A solution of the two dimensional Global Asymptotic Jacobian Stability Conjecture, Preprint. ETH-Zentrum, Switzerland.

[4] A. Gasull, J. Llibre and J. Sotomayor, Global asymptotic stability of differential equations in the plane, J. diff. Eq., 1989, To appear. | MR 1111178 | Zbl 0732.34045

[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. | MR 1094380 | Zbl 0713.34053

[6] G. Gorni and G. Zampieri, On the global conjecture for global asymptotic stability, 1990, To appear.

[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. | MR 1179484 | Zbl 0776.34024

[8] P. Hartman, On stability in the large for systems of ordinary differential equations, Can. J. Math., Vol. 13, 1961, pp. 480-492. | MR 123791 | Zbl 0103.05901

[9] P. Hartman, Ordinary differential equations, Sec. Ed. Birkhäuser, 1982. | MR 658490 | Zbl 0476.34002

[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. | MR 88420

[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] L. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Math. J., Vol. 12, 1960, pp. 305-317. | MR 126019 | Zbl 0096.28802

[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. | Zbl 0854.34054

[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. | MR 956968 | Zbl 0668.34048

[15] C. Olech, On the global stability of an autonomous system on the plane, Cont. to Diff. Eq., Vol. 1, 1963, pp. 389-400. | MR 147734 | Zbl 0136.08602

[16] B. Smith and F. Xavier, Injectivity of local diffeomorphisms from nearly spectral conditions, University of Notre Dame, Preprint, 1993.