Moscow Mathematical Journal
Volume 23, Issue 4, October–December 2023 pp. 533–544.
Gradient-Like Diffeomorphisms and Periodic Vector Fields
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, 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 $\mathrm{id}_M$, 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. 2020 Math. Subj. Class. 34C40, 37B35, 37C60
Authors:
V.Z. Grines (1) and L.M. Lerman (2)
Author institution:(1) National Research University, “Higher School of Economics” (Nizhny Novgorod branch)
(2) National Research University, “Higher School of Economics” (Nizhny Novgorod branch)
Summary:
Keywords: Nonautonomous vector field, uniform equivalence, exponential dichotomy, gradient-like, nonautonomous suspension.
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