ATTRACTORS OF LOCAL SEMIFLOWS ON TOPOLOGICAL SPACES
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In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.
Abstract
In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.
참고문헌 (22)
- A. V. Babin, "Attractors of Evolution Equations" (1992), North-Holland
- N. P. Bhatia, "Local Semi-dynamical Systems" (1969), Springer-Verlag
- D. N. Cheban, "Global Attractors of Non-autonomous Dissipative Dynamical Systems" (2004), World Scientific Publishing Co. Pte. Ltd
- V. V. Chepyzhov, "Attractors of Equations of Mathematical Physics" (2002), Amer. Math. Soc
- F. Gazzola, "Attractors for families of processes in weak topologies of Banach spaces", Discrete Contin. Dyn. Syst, 4(3), pp.455~466 (1998)
- A. Giraldo, "Shape of global attractors in topological spaces", Nonlinear Anal, 60(5), pp.837~847 (2005)
- W. H. Gottschalk, "Topological Dynamics" (1955), Amer. Math. Soc
- J. K. Hale, "Asymptotic Behavior of Dissipative Systems" (1998), Amer. Math. Soc
- L. Kapitanski, "Shape and Morse theory of attractors", Commun. Pure Appl. Math, 53(2), pp.218~242 (2000)
- O. A. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations, Lizioni Lin-cei" (1991), Cambridge Univ. Press
- "A linking theory of dynamical systems with appli-cations to PDEs"[URL]
- D. S. Li, "Smooth Morse-Lyapunov functions of strong attractors for dif-ferential inclusions", SIAM J. Control Optim, 50(1), pp.368~387 (2012)
- Q. F. Ma, "Necessary and sufficient conditions for the existence of global attractors for semigroups and applications", Indiana Univ. Math. J, 51(6), pp.1541~1559 (2002)
- L. Markus, "The global theory of ordinary differential equations", Lecture Notes, Univ. Minnesota, ~ (1964)
- A. Marzocchi, "Attractors for dynamical systems in topological spaces", Discrete Contin. Dyn. Syst, 8(3), pp.585~597 (2002)
- J. C. Robinson, "Infinite-dimensional Dynamical Systems" (2001), Cambridge University Press
- K. P. Rybakowski, "The Homotopy Index and Partial Differential Equations" (1987), Springer-Verlag
- G. R. Sell, "Nonautonomous Differential Equations and Topological Dynamics I. The basic Theory", Trans. Amer. Math. Soc, 127, pp.241~262 (1967)
- G. R. Sell, "Dynamics of Evolutionary Equations" (2002), Springer-Verlag
- R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics" (1997), Springer-Verlag
- M. I. Vishik, "Asymptotic Behavior of Solutions of Evolutionary Equations" (1992), Cambridge Univ. Press
- J. T. Wang, "On the shape conley index theory of semiflows on complete metric spaces", Discrete Contin. Dyn. Syst, 36(3), pp.1629~1647 (2016)