DOI QR코드

DOI QR Code

STABLE INDEX PAIRS FOR DISPERSIVE DYNAMICAL SYSTEMS

  • Goo, Yoon-Hoe ;
  • Park, Jong-Suh
  • 투고 : 2009.05.07
  • 발행 : 2011.01.31

초록

We construct the index pairs of an isolated neighborhood for a dispersive dynamical system and investigate the existence of an index pair which is stable under small perturbations of the dispersive dynamical systems.

키워드

index pair;dispersive dynamical systems;I-solution;isolating neighborhood

참고문헌

  1. R. Churchill, Isolated invariant sets in compact metric spaces, J. Differential Equations 12 (1972), 330-352. https://doi.org/10.1016/0022-0396(72)90036-8
  2. C. C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. Math. No. 38, Amer. Math. Soc., Providence RI, 1978.
  3. E. N. Dancer, Perturbation of zeros in the presence of symmetries, J. Austral. Math. Soc. Ser. A 36 (1984), no. 1, 106-125. https://doi.org/10.1017/S1446788700027361
  4. E. N. Dancer, Degenerate critical points, homotopy indices and Morse inequalities, J. Reine Angew. Math. 350 (1984), 1-22.
  5. A. Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965), 1-8. https://doi.org/10.1016/0040-9383(65)90044-3
  6. T. Kaczynski and M. Morzec, Conley index for discrete multi-valued dynamical systems, Topology Appl. 65 (1995), no. 1, 83-96. https://doi.org/10.1016/0166-8641(94)00088-K
  7. T. Kaczynski and M. Morzec, Stable index pairs for discrete dynamical systems, Canad. Math. Bull. 40 (1997), no. 4, 448-455. https://doi.org/10.4153/CMB-1997-053-2
  8. P. E. Kloeden, Asymptotic invariance and limit sets of general control systems, J. Differential Equations 19 (1975), no. 1, 91-105. https://doi.org/10.1016/0022-0396(75)90021-2
  9. H. L. Kurland, The Morse index of an isolated invariant set is a connected simple system, J. Differential Equations 42 (1981), no. 2, 234-259. https://doi.org/10.1016/0022-0396(81)90028-0
  10. D. Li, On dynamical stability in general dynamical systems, J. Math. Anal. Appl. 263 (2001), no. 2, 455-478. https://doi.org/10.1006/jmaa.2001.7620
  11. J. T. Montgomery, Cohomology of isolated invariant sets under perturbation, J. Differential Equations 13 (1973), 257-299. https://doi.org/10.1016/0022-0396(73)90018-1
  12. E. Roxin, Stability in general control systems, J. Differential Equations 1 (1965), 115-150. https://doi.org/10.1016/0022-0396(65)90015-X
  13. K. Rybakowski, On the homotopy index for infinite dimensional semiflows, Trans. Amer. Math. Soc. 269 (1982), no. 2, 351-382. https://doi.org/10.1090/S0002-9947-1982-0637695-7
  14. K. S. Sibirsky, Introduction to Topological Dynamics, Noordhoff International Publishing, Leiden, 1975.
  15. H. Siegberg and G. Skordev, Fixed point index and chain approximations, Pacific J. Math. 102 (1982), no. 2, 455-486. https://doi.org/10.2140/pjm.1982.102.455

과제정보

연구 과제 주관 기관 : Hanseo University