ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 58F Gan, Shaobo, School of mathematical science, Peking University, China Star Systems X^{∗} and a Proof of The C^{1} Ω Stability In this paper we give a new proof for the C^{1} Ω stability conjecture for flows. Our approach is considerably different from that of Hayashi or Wen, and a good deal of Liao’s obstruction sets theory is used. Ref. S. Hayashi, Connecting invariant manifolds and the solution of the C^{1} stability conjecture and Ω-stability conjecture for flows. Annals of Math. 145 (1997), 81-137. S. T. Liao, The qualitative theory of differential dynamical systems, Science Press, 1996. L. Wen, on the C^{1} stability conjecture for flows, J. D. E (129) (1996), 334–357.