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One-dimensional monotone nonautonomous dynamical systems

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Abstract

This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous (cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets, Bohr/Levitan almost periodic and almost automorphic motions, global attractors, pinched and minimal sets is given. An application of our general results is given to scalar differential and difference equations.

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Acknowledgements

This work was supported by the State Program of the Republic of Moldova “Multivalued Dynamical Systems, Singular Perturbations, Integral Operators and Non-Associative Algebraic Structures (Grant No. 20.80009.5007.25)”. The author thanks the referees for their comments and suggestions which improved the quality of the paper.

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  1. Faculty of Mathematics and Computer Science, Laboratory of Fundamental and Applied Mathematics, Moldova State University, Chisinau, 2009, Republic of Moldova

    David Cheban

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Cheban, D. One-dimensional monotone nonautonomous dynamical systems. Sci. China Math. 67, 281–314 (2024). https://doi.org/10.1007/s11425-021-2084-x

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