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Topological cocycles

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Abstract

In this essay we consider topological cocycles via semibornology and group structures. Global and local attractors via semibornological nonautonomous sets are studied. We show that global semibornological pullback attractors are compact and positively invariant. We introduce the concept of global \((g,\beta )\) pullback attractors and we show that they are also compact and positively invariant. We prove that semibornological pullback attractors are invariant objects under topological equivalencies. We present a method for finding absorbing sets when the state space of the dynamical system of a cocycle is a convex semibornological vector space.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer, Mahani Mathematical Research Center and Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    M. R. Molaei

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  1. M. R. Molaei
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Correspondence to M. R. Molaei.

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Molaei, M.R. Topological cocycles. Bol. Soc. Mat. Mex. 24, 257–267 (2018). https://doi.org/10.1007/s40590-016-0158-y

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  • DOI: https://doi.org/10.1007/s40590-016-0158-y

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