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Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems

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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.

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Authors and Affiliations

  1. State University of Moldova, A. Mateevich str. 60, MD–2009, Chişinău, Moldova

    David Cheban

  2. University of Macerata, str. Crescimbeni 14, I–62100, Macerata, Italy

    Cristiana Mammana

Authors
  1. David Cheban
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  2. Cristiana Mammana
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Correspondence to David Cheban.

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Dedicated to our friend Professor Enrico Primo Tomasini on the occasion of his 55th birthday

Mathematics Subject Classifications (2000)

Primary: 34C35, 34D20, 34D40, 34D45, 58F10,58F12, 58F39; secondary: 35B35, 35B40.

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Cheban, D., Mammana, C. Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems. Set-Valued Anal 13, 291–321 (2005). https://doi.org/10.1007/s11228-004-0046-x

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