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<p>We construct an example of a multidimensional autonomous differential system such that all its solutions tend to zero with time. For the solutions starting in a ball centered at zero and leaving the ball at a sufficient distance with time the relative measure of the initial values becomes arbitrarily close to 1 as the ball radius tends to zero. We show that the constructed system possesses the zero linear approximation along the zero solution. Bibliography: 7 titles. Illustrations: 1 figure.</p>

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AUTONOMOUS DIFFERENTIAL SYSTEM WITH CONTRASTING COMBINATIONS OF GLOBAL STABILITY PROPERTIES AND MEASURES

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Alexey Bondarev

摘要

We construct an example of a multidimensional autonomous differential system such that all its solutions tend to zero with time. For the solutions starting in a ball centered at zero and leaving the ball at a sufficient distance with time the relative measure of the initial values becomes arbitrarily close to 1 as the ball radius tends to zero. We show that the constructed system possesses the zero linear approximation along the zero solution. Bibliography: 7 titles. Illustrations: 1 figure.