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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.
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참고문헌 (22)
참고문헌 신청
A. Giraldo / 2005 / Shape of global attractors in topological spaces / Nonlinear Anal 60 (5) : 837 ~ 847
A. Marzocchi / 2002 / Attractors for dynamical systems in topological spaces / Discrete Contin. Dyn. Syst 8 (3) : 585 ~ 597
A. V. Babin / 1992 / Attractors of Evolution Equations / North-Holland
D. N. Cheban / 2004 / Global Attractors of Non-autonomous Dissipative Dynamical Systems / World Scientific Publishing Co. Pte. Ltd
D. S. Li / / A linking theory of dynamical systems with appli-cations to PDEs
A. Marzocchi / 2002 / Attractors for dynamical systems in topological spaces / Discrete Contin. Dyn. Syst 8 (3) : 585 ~ 597
A. V. Babin / 1992 / Attractors of Evolution Equations / North-Holland
D. N. Cheban / 2004 / Global Attractors of Non-autonomous Dissipative Dynamical Systems / World Scientific Publishing Co. Pte. Ltd
D. S. Li / / A linking theory of dynamical systems with appli-cations to PDEs
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