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首页> 外文期刊>Discrete and continuous dynamical systems >NONAUTONOMOUS GRADIENT-LIKE VECTOR FIELDS ON THE CIRCLE: CLASSIFICATION, STRUCTURAL STABILITY AND AUTONOMIZATION
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NONAUTONOMOUS GRADIENT-LIKE VECTOR FIELDS ON THE CIRCLE: CLASSIFICATION, STRUCTURAL STABILITY AND AUTONOMIZATION

机译：圆圈上的非编程渐变矢量字段：分类，结构稳定性和自主性

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摘要

We study a class of scalar differential equations on the circle S~1. 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.
机译：我们研究了一类圆圈S〜1上的标量子微分方程。该课程的特征主要是由这种等式的任何解决方案的性质具有指数二分术，在半轴R_ +和R_ +上。此外，我们对这种等式的整体曲线施加了一些其他假设。此类的微分方程称为梯度样式。因此，我们描述了叶子的全局行为，引入了统一等效的完整不变，为此杰出类的等式提供标准模型。还研究了几乎周期性梯度等方程的情况，提出了它们的分类。

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