Moscow Mathematical Journal
Volume 23, Issue 4, October–December 2023 pp. 533–544.
Gradient-Like Diffeomorphisms and Periodic Vector Fields
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:
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 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.
2020 Math. Subj. Class. 34C40, 37B35, 37C60
Keywords: Nonautonomous vector field, uniform equivalence, exponential dichotomy, gradient-like, nonautonomous suspension.
Contents Full-Text PDF