Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems |
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Authors: | David Cheban and Cristiana Mammana |
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Institution: | (1) State University of Moldova, A. Mateevich str. 60, MD–2009 Chişinău, Moldova;(2) University of Macerata, str. Crescimbeni 14, I–62100 Macerata, Italy |
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Abstract: | 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.
Dedicated to our friend Professor Enrico Primo Tomasini on the occasion of his 55th birthdayMathematics Subject Classifications (2000) Primary: 34C35, 34D20, 34D40, 34D45, 58F10,58F12, 58F39; secondary: 35B35, 35B40. |
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Keywords: | global attractor set-valued dynamical systems forward pullback and trajectory attractors absolute asymptotic stability |
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