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Continuity of the orbital and limit set maps in general dynamical systems

박종서|이경복
대한수학회 (The Korean Mathematical Society)|2011.10|대한수학회논문집 (Communications of the KMS)|제26권 제4호|pp. 649-660

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참고문헌

키워드

general dynamical systemslower and upper semicontinuouscontinuity and stabilitymotion and limit setminimality and charactorstic O^+
주제분류수학

초록

S. M. Saperstone and M. Nishihama [6] had showed both continuity and stability of the orbital and limit set maps,K(x) and L(x), where K and L are considered as maps from X to 2^X. The main purpose of this paper is to extend continuity and stability for dynamical systems to general dynamical systems.

Abstract

S. M. Saperstone and M. Nishihama [6] had showed both continuity and stability of the orbital and limit set maps,K(x) and L(x), where K and L are considered as maps from X to 2^X. The main purpose of this paper is to extend continuity and stability for dynamical systems to general dynamical systems.

참고문헌 (7)

  1. N. P. Bhatia, "Stability Theory of Dynamical Systems" (1970), Springer Verlag
  2. S. Elaydi, "Asymptotic stability in general dynamical systems", Nonlinear Anal, 13(6), pp.657~669 (1989)
  3. D. Li, "Morse decompositions for general dynamical systems and differential inclusions with applications to control systems", SIAM J. Control Optim, 46(1), pp.35~60 (2007)
  4. D. Li, "On dynamical stability in general dynamical systems", J. Math. Anal. Appl, 263(2), pp.455~478 (2001)
  5. E. Roxin, "Stability in general control system", J. Differential Equations, 1, pp.115~150 (1965)
  6. S. H. Saperstone, "Continuity of the limit set maps in semidynamical systems", J. Differential Equations, 23(2), pp.183~199 (1977)
  7. K. S. Sibirsky, "Introduction to Topological Dynamics" (1975), Noordhoff international Pub. Ley- den

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