ArticleOriginal scientific text
Title
Global attractor of a differentiable autonomous system on the plane
Authors 1
Affiliations
- Institute of Mathematics, Hanoi P.o. Box 631 10000 Boho, Hanoi, Vietnam
Abstract
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.
Keywords
Markus-Yamabe Conjecture, asymptotically stable, Jacobian Conjecture
Bibliography
- V. I. Arnold and Yu. S. Il'yashenko, Ordinary differential equations. I, in: Dynamical Systems I, Ordinary Differential Equations and Smooth Dynamical Systems, D. V. Anosov and V. I. Arnold (eds.), Springer, New York, 1988, 7-149.
- H. Bass, E. F. Connell and D. Wright, The Jacobian Conjecture, Bull. Amer. Math. Soc. 7 (1982), 287-330.
- A. Białynicki-Birula and M. Rosenlicht, Injective morphisms of algebraic varieties, Proc. Amer. Math. Soc. 13 (1962), 200-204.
- O. H. Keller, Ganze Cremona-Transformationen, Monatsh. Math. Phys. 47 (1939), 299-306.
- L. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Math. J. 12 (1960), 305-317.
- D. J. Newman, One-one polynomial maps, Proc. Amer. Math. Soc. 11 (1960), 867-870.
- C. Olech, On the global stability of an autonomous system on the plane, in: Contributions to Differential Equations 1 (1963), 389-400.
- C. Olech, Global phase-portrait of a plane autonomous system, Ann. Inst. Fourier (Grenoble) 14 (1964), 87-98.
- C. Olech and M. Meisters, Solution of the global asymptotic stability Jacobian Conjecture for the polynomial case, in: Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988, 373-381.
Pages:
143-154
Main language of publication
English
Received
1994-10-20
Published
1995
Exact and natural sciences