Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems
Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems
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DOI：
10.1007/s11228-004-0046-x
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发表时间：
2005-09
期刊：
影响因子：
--
通讯作者：
D. Cheban;C. Mammana
中科院分区：
文献类型：
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作者：
D. Cheban;C. Mammana
研究了集值非自治动力系统（共环）的正向吸引子与回拉吸引子之间的关系。证明了集值非自治动力系统的每一个紧致全局正向吸引子也是一个回拉吸引子。一般来说，逆命题是不成立的，但我们证明了α-凝聚集值循环的每一个全局回拉吸引子总是一个局部正向吸引子。所得的一般结果应用于周期系统和齐次系统的研究。给出了非平稳离散线性包含的绝对渐近稳定性的一个新判据。
The article is devoted to the study of the relation between forward and pullback attractors of set-valued nonautonomous dynamical systems (cocycles). Here it is proved that every compact global forward attractor is also a pullback attractor of the set-valued nonautonomous dynamical system. The inverse statement, generally speaking, is not true, but we prove that every global pullback attractor of an α-condensing set-valued cocycle is always a local forward attractor. The obtained general results are applied while studying periodic and homogeneous systems. We give also a new criterion of the absolute asymptotic stability of nonstationary discrete linear inclusions.