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Nonautonomous gradient-like vector fields on the circle: classification, structural stability and autonomization
Discrete and Continuous Dynamical Systems - Series S. 2020. Vol. 13. No. 4. P. 1341-1367.
Lerman L., Gubina E.
We study a class of scalar differential equations on the circle S1. This class is characterized mainly by the property that any solution of such an equation possesses an exponential dichotomy both on the semi-axes R+ and R+. Also we impose some other assumptions on the structure of the foliation into integral curves for such the equation. Differential equations of this class are called gradient-like ones. As a result, we describe the global behavior of
a foliation, introduce a complete invariant of the uniform equivalency, give standard models for the equations of this distinguished class. The case of almost periodic gradient-like equations is also studied, their classification is
presented.
Keywords: classificationuniform continuitynonautonomous perturbationdichotomyquasi-periodic oscillations
Publication based on the results of:
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