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Existence of a Right System whose Upper-Limit Central and General Indexes do not Coincide with Lower-Limit Ones
Moscow University Mathematics Bulletin Pub Date : 2019-05-04 , DOI: 10.3103/s0027132219020098
V. I. Kokushkin

On the one hand, we show that the upper-limit analogues of Vinograd-Millionshchikov central exponents determined on the space of regular linear differential systems are equal to lower-limit ones. A similar fact is also valid for analogues of Bohl-Persidsky general exponents on the space of almost reducible systems. On the other hand, we present an example of a two-dimensional regular differential system with bounded piecewise continuous coefficients having noncoinciding upper-limit and lower-limit central and general exponents.

中文翻译:

上限中央指标和一般指标与下限指标不一致的权利系统的存在

一方面,我们表明在规则线性微分系统的空间上确定的维诺格拉德-米利什科夫中心指数的上限类似物等于下限。在几乎可约化系统的空间上,类似的事实对于Bohl-Persidsky一般指数的类似物也是有效的。另一方面,我们给出了一个二维正则微分系统的示例,该系统具有有限的分段连续系数,其上限和下限的中心指数和总指数不一致。
更新日期:2019-05-04
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