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Gradient-Like Diffeomorphisms and Periodic Vector Fields
Moscow Mathematical Journal. 2023. Vol. 23. No. 4. P. 533–544.
A class of gradient-like nonautonomous vector fields (NVFs) on a smooth closed manifold M is studied and the following problems are solved: 1) can a gradient-like NVF be constructed by means of the nonautonomous suspension over a diffeomorphism of this manifold, and if so, 1) under what conditions on the diffeomorphism? 2) let a diffeomorphism f be gradient-like (see the definition in the text) and diffeotopic to the identity map idM, when the NVF obtained by means of the nonautonomous suspension over f be gradient-like? Necessary and sufficient conditions to this have been found in the paper. All these questions arise, when studying NVFs on M admitting the uniform classification and a description via combinatorial type invariants.
Keywords: suspension flowgradient-like cascadeexponential dichotomynonautonomous vector fielduniform equivalence
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