Geodesic
An example of complete but not global Perron instability
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 43-47

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Various properties of the two-dimensional differential system related to Perron stability are studied. It is proved that, generally speaking, the global Perron instability doesn't follow from the total Perron instability, while this may seem at first glance. It turns out that it is possible to construct a counter-example even with an infinitely differentiable right-hand side and a zero matrix of the first approximation at zero. The system considered here is nonlinear. 
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     author = {A. A. Bondarev},
     title = {An example of complete but not global {Perron} instability},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {43--47},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a8/}
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A. A. Bondarev. An example of complete but not global Perron instability. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 43-47. http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a8/