On the Omega Limit Sets for Analytic Flows

• Journal title : Kyungpook mathematical journal
• Volume 54, Issue 2,  2014, pp.333-339
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2014.54.2.333
Title & Authors
On the Omega Limit Sets for Analytic Flows
Choy, Jaeyoo; Chu, Hahng-Yun;

Abstract
In this paper, we describe the characterizations of omega limit sets (
Keywords
attractors;$\small{{\omega}}$-limit sets;analytic flows;
Language
English
Cited by
1.
A TOPOLOGICAL CHARACTERIZATION OF ­Ω-LIMIT SETS ON DYNAMICAL SYSTEMS,;;;

충청수학회지, 2014. vol.27. 3, pp.523-530
1.
A TOPOLOGICAL CHARACTERIZATION OF ­Ω-LIMIT SETS ON DYNAMICAL SYSTEMS, Journal of the Chungcheong Mathematical Society, 2014, 27, 3, 523
References
1.
A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maier, Qualitative theory of second-order dynamic systems, Translated from the Russian by D. Louvish. Halsted Press (A division of John Wiley & Sons), New York-Toronto, Ont., Jerusalem-London, 1973.

2.
V. I. Arnol'd and Y. S. Il'yashenko, Ordinary differential equations, [Current problems in mathematics. Fundamental directions, Vol. 1, 7-149, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1985; MR0823489 (87e:34049)]. Translated from the Russian by E. R. Dawson and D. O'Shea. Encyclopaedia Math. Sci., 1, Dynamical systems, I, 1-148, Springer, Berlin, 1988.

3.
J. Choy and H.-Y. Chu, Attractors on Riemann spheres, submitted.

4.
J. Choy and H.-Y. Chu, On the Envelopes of Homotopies, Kyungpook Math. J., 49(3)(2009), 573-582

5.
C. M. Carballo and C. A. Morales, Omega-limit sets close to singular-hyperbolic at-tractors, Illinois J. Math., 48(2004), 645-663.

6.
C. Conley, Isolated invariant sets and the morse index, C. B. M. S. Regional Lect., 38, A. M. S., 1978

7.
F. Dumortier, Singularities of vector fields on the plane, J. Differential Equations, 23(1977), 53-106.

8.
F. Rodriguez Hertz and J. Rodriguez Hertz, Expansive attractors on surfaces, Ergodic Theory Dynam. Systems, 26(2006), 291-302.

9.
V. Jimenez Lopez and J. Llibre, A topological characterization of the !-limit sets for analytic flows on the plane, the sphere and the projective plane, Adv. Math., 216(2007), 677-710.

10.
V. Jimenez Lopez and D. Peralta-Salas, Global attractors of analytic plane flows, To appear in Ergodic Theory Dynam. Systems.

11.
C. A. Morales, M. J. Pacifico and E. R. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers, Ann. of Math., 160(2004), 375-432.

12.
J. Milnor, On the concept of attractor, Commun. Math. Phy., 99(1978), 177-195.

13.
J. C. Robinson and O. M. Tearne, Boundaries of attractors of omega limit sets, Stoch. Dyn., 5(2005), 97-109.

14.
A. Seidenberg, Reduction of singularities of the differential equation Ady = Bdx. Amer. J. Math., 90(1968), 248-269.