![](data:image/png;base64,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)
.
Картина расположения траекторий при
![](data:image/png;base64,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)
, имеющая специальное название — узел, изображена на рис. 1а.
2)
![](data:image/png;base64,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)
вещественны и
![](data:image/png;base64,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)
. Полученные в случае узла формулы сохраняют силу. Соответствующая геометрическая картина, называемая седлом, изображена на рис. 1б.
3)
![](data:image/png;base64,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)
комплексно-сопряженные. Пусть
![](data:image/png;base64,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)
. В преобразовании X = SY
![](data:image/png;base64,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)
, где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAVCAMAAAB44J7gAAAAAXNSR0ICQMB9xQAAAEhQTFRFAAAAAQEBIiJOIyNPTiIiTyMjTDVdQ1h4Xn6XeFhDl35ekHeEmay9vayZv7i42c7Cws7Z5uPc/v7++fn47/Ly+Pn58vLv////2sa50gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABZSURBVCjPYxBHAwz4BIRQBYQ5mURQVQhzU1dASAhoJRcjuyhUQIyFkYEH2WG8HOL8AsgCgmwiaE7nB+lGCPCJinPxIAkIcwoIcXEgCYixMjIyixAVHkQKAACgXxwE5RSTXQAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAVCAMAAACXIvXeAAAAAXNSR0ICQMB9xQAAAE5QTFRFAAAAAQEBIyNPTiIiTyMjTDVdQ1h4Xn6XeFhDaURpl35emay9pI6CvayZv7i4zsHB2c7Cws7Z3OPm5uPc/v7+8vLv7/Ly+Pn5+fn4////I7OF7AAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPjdDLEoAgCAVQ6WVplhZi/f+PZlOTyqKR5VlwL4iTj/gVRCa+BV3KSn4ivmfeuCyBiXUsy0r8BO9gAwDulZgrdNHQyGdFkr0nfoUdQiGxhdK5HKNDJXPxHUBDlf+plwvHVyAj1mGENgAAAABJRU5ErkJggg==)
— линейно независимые собственные векторы, соответствующие
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAXCAMAAADa6lTVAAAAAXNSR0ICQMB9xQAAAFpQTFRFAQEBFBQvLhMTIiJOIyNPTiIiQ1h4Xn6XeFhDaWmGl35ekHeEgo6kmZmtmay9rZmZvayZuLi/r7fGxrevzca5wcHOws7Z3OPm5uPc8vLv+Pn57/Ly+fn4////xwhwBQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABmSURBVCjPrdBJDoAgDAXQOoCKE07Mvf81RUxUWBL/pslL2zQFTAM/CoMmFrXiJtMpfaSihlQYNbGosrOxcLqLSDQRn9UQWoxbfHVtZYNoMiHOVo/o+lt4ba/lhXzkTZ4w8Lfn/fAEn2QpLNO53A0AAAAASUVORK5CYII=)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAMAAAA8w5+RAAAAAXNSR0ICQMB9xQAAAGNQTFRFAAAAAQEBFBQvLhMTIyNPTiIiQ1h4Xn6XaURpaWmGl35ego6kmZmtmay9rZmZpI6CvayZuLi/v7i4r7fGxrevzca5wcHOws7ZzsHB2c7C3OPm5uPc8vLv+Pn57/Ly+fn4////BbCm4QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB2SURBVCjPtdDLEsIgDAXQYKVUfNGXCISU//9KW3RTk50jq8yZZEIuFOHBn9AqwzCNZYrCOD4ETGcBbZsZpuZEDF07+29E7feboDbmpa+f0Or6QdRrdSO8lCdhR290R9p2HeoB9yjcPmSOwfOUguHROQDlf0/+BS6pNa3bMUxHAAAAAElFTkSuQmCC)
. Так как А вещественна,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAVCAMAAAB44J7gAAAAAXNSR0ICQMB9xQAAAEhQTFRFAAAAAQEBIiJOIyNPTiIiTyMjTDVdQ1h4Xn6XeFhDl35ekHeEmay9vayZv7i42c7Cws7Z5uPc/v7++fn47/Ly+Pn58vLv////2sa50gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABZSURBVCjPYxBHAwz4BIRQBYQ5mURQVQhzU1dASAhoJRcjuyhUQIyFkYEH2WG8HOL8AsgCgmwiaE7nB+lGCPCJinPxIAkIcwoIcXEgCYixMjIyixAVHkQKAACgXxwE5RSTXQAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAVCAMAAACXIvXeAAAAAXNSR0ICQMB9xQAAAE5QTFRFAAAAAQEBIyNPTiIiTyMjTDVdQ1h4Xn6XeFhDaURpl35emay9pI6CvayZv7i4zsHB2c7Cws7Z3OPm5uPc/v7+8vLv7/Ly+Pn5+fn4////I7OF7AAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPjdDLEoAgCAVQ6WVplhZi/f+PZlOTyqKR5VlwL4iTj/gVRCa+BV3KSn4ivmfeuCyBiXUsy0r8BO9gAwDulZgrdNHQyGdFkr0nfoUdQiGxhdK5HKNDJXPxHUBDlf+plwvHVyAj1mGENgAAAABJRU5ErkJggg==)
можно выбрать комплексно-сопряженными. Тогда и
![](data:image/png;base64,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)
. Положим
![](data:image/png;base64,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)
,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAAXCAMAAAB9N+IuAAAAAXNSR0ICQMB9xQAAAIdQTFRFAAAAAQEBExMuFBQvLxQUPyY/IyNPIiJOTyMjTiIiQ1h4Xn6XeFhDaURpaWmGl35ehmlpkHeEhHeQg5ubgo6kmay9pI6CpZulvayZv7i4r7fG2c7Cws7ZwcHOzsHByMjB0NDQ3OPm5t/f5uPc/v7+7/Ly+Pn5+fn48vLv7Orn5+rs8PLw////cF3vLQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEFSURBVEjH7ZTrEoIgEIWhe2nZPQu7mCBWvP/zRbDekGzGaepH7YzOyHI+9uw6IPHeQH/eV3n0vTy/xz7hl75yJcO+biYVz0OjWBD5lADZNu5ijFphFZcMUGAkdX2kzwTf5DwP63DU1+UqVwLbWXzGjKTmRd1QJPsawwVF8axoaSSBlwwDcWAi70PJLygsHfRXGQ42Z7xoJ994ZfOrFNztMxPHp2GKS7UIOr6Yx7LCZMysZik9M9mryjzGx1AnM23Kg/9ybZmiryu18Ah2/NyG0sL/fIId2/jpSCy8ciit5EWTmwsTIoFozNPaB6/TBpfEoY15oEVGo54X6OFRXHMxgPbX7uc7GWIi06g/P7MAAAAASUVORK5CYII=)
, а в качестве фазовой плоскости возьмем
![](data:image/png;base64,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)
. Переменная
![](data:image/png;base64,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)
связана с Х соотношением X = SY = = STZ = QZ, где
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Следовательно, Q — вещественная неособая матрица. Преобразование приводит к виду
![](data:image/png;base64,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)
где матрица коэффициентов образует вещественную жорданову форму матрицы А.
Введем полярные координаты
![](data:image/png;base64,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)
, или
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Имеем:
![](data:image/png;base64,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)
. Отделяя вещественные и мнимые части, получим:
![](data:image/png;base64,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)
.
Следовательно,
![](data:image/png;base64,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)
. При
![](data:image/png;base64,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)
траектории образуют спирали (рис. 1в). Такое положение траекторий называется фокусом. При
![](data:image/png;base64,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)
все траектории — окружности. В этом случае получаем центр. В случае центра все решения системы (3) периодические с периодом 2/.
4)
![](data:image/png;base64,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)
. Жорданова форма матрицы А имеет треугольный вид, а система преобразуется к виду
![](data:image/png;base64,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)
Решением этой системы будет функция
![](data:image/png;base64,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)
. В зависимости от формы матрицы J получаются два случая: или вырожденный узел (рис. 1г), либо звездный (дикритический) узел. Дикритический узел возможен лишь в случае системы
![](data:image/jpeg;base64,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)
Рис. 1. Поведение траекторий в зависимости от значений собственных чисел
1.5. Линейные однородные системы с периодическими коэффициентами.
В данном пункте излагается так называемая теория Флоке.
Будем рассматривать систему вида
![](data:image/png;base64,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)
(4)
где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAAAYCAMAAAAyNwimAAAAAXNSR0ICQMB9xQAAAKVQTFRFAAAAAQEBFBQvExMuLhMTPyY/IiJOIyNPTyMjTiIiTDVdXTVMQCdAQ1h4RFl5Xn6XeFhDaURpakVqaWlEl35ehmlpkHeEm5CQmZmtmay9pI6CrZmZvayZr6+vr7fGws7Z2c7Cwc3YzsHB2M3B3+bf3OPm2+Ll4NfT5uPc5eLb/v7+8fHu7/Ly8vLv7vHx8/Hx+fn48PLw+Pn5+Pj35uvp9/j4////mdmSPgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAG3SURBVEjH7VXtUoMwEEz6YWm10ipVY1GiNjWNBLFV3v/RvEsCBIbyr+OMms5AJ7nbzd5tAilOPMg/wc8RKPh5BEqp6mlXqled4kY/rguQs03AaoKYEpoUMSEDURRvyxTn9DJrpEaUEEopOct68HcjSifZqyjeH243d54CPgRkbTj5JLVzciwayXIEQfmCDMVR/IhAsg4gQq8S7imAPFbkN6nZuMGXjygz9bP1FKHliLAm6n1FGJMzzMhXogD0deY3OZ5/rExgZNJ34y1Ohn4zKoKkSSBNrAkgNgFKtE51cLn3CLhTrs+FkYo9cRI4ZSXBVh0WNGwXJh5uHUab2yPQU7vGjUino5ysNgh9DtumUkBKnmyFjhPo5bXNjA2B1QGQrNWDqMLgtB5Wb58C6KxFdgTxfN9N0GmifGHwsT1hNwE635nSlAg91VUiwAYQS+73YCBKl9pdPqcNAvWC04cFU2Vx5OzTWNb5VJWHCJqMdWDNw1y7WQdk/qVUxBoKdEDBJvg0G8FVbv86mzoXRVhtcF7kAjvOAV4JMJLey871t6zcCW5TeSFKwclprmt9lXqvv/vB+TUE362RskoUg9x+AAAAAElFTkSuQmCC)
, а матричная функция P(t) удовлетворяет условию P(t + ) = P(t), >0 при всех
![](data:image/png;base64,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)
. Такие матричные функции будем называть периодическими с периодом или -периодическими.
Теорема Флоке. Фундаментальная матрица системы (4) имеет вид
![](data:image/png;base64,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)
где G — -периодическая матрица, R — постоянная матрица.
Матрица В, определяемая равенством
![](data:image/png;base64,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)
, называется матрицей монодромии. Для нее справедливо
![](data:image/png;base64,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)
. Она определяется с помощью фундаментальной матрицы неоднозначно, но можно показать, что все матрицы монодромии подобны. Часто матрицей монодромии называют ту, которая порождается нормированной при
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAATCAMAAAApiJT7AAAAAXNSR0ICQMB9xQAAAGBQTFRFAAAAAQEBFBQvLhMTPyY/IiJOTiIiXTVMTDVdQ1h4Xn6XeFhDl35ekHeEmay9vayZr7fGws7Z2c7C2+Ll3OPm5uPc5eLb/v7+7/Ly8vLv+fn4+Pn55+zq9/j48fHu////nWq6SwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACHSURBVCjPvZFJDoAgDEXBeUBRBHHm/rdUoZqIRhMT/Qs2vPLagtRT0LeElA8Exbi8JZjftEG5E6KwgS5dblncA1F7lU0Ij8OxEgQho5QmIFFKa/QbJNd1BJskJ6IN+VWji8UFgq4NWZZDH11qJAeLnoXCLCIasuasicdp2wfDDn+z079+HzIDJ2NDsGwCKHAAAAAASUVORK5CYII=)
фундаментальной матрицей
![](data:image/png;base64,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)
, то есть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAZCAMAAABZ9LPtAAAAAXNSR0ICQMB9xQAAAIFQTFRFAAAAAQEBFBQvExMuLxQULhMTPyY/IiJOIyNPTiIiTyMjTDVdXTVMQ1h4Xn6XeFhDaURpl35eiop3jJOMmay9rZmZpZulvayZr6+vws7Z2c7CytXPwcHOzsHB3OPm2+Ll5uPc5eLb/v7++Pj3+Pn57/Ly8vLv+fn47vHx8fHu////zqyatgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFVSURBVDjL3ZTrUoMwEIUTkSJVglE0JmoL2ybVvP8Dmt1wm5YWa3/VzMC0TDj77dlDmL90sWtQAIDLFOpbzgXA5nX7V4UX673i/GY1xwAnYGf6iAqSsQA7vUNyxorYg3u0/eP+d8ugMutyMU3QpDpSmMyOHVqsxgpS+F1ZTLjVpJwHvmQ9VAWURYl7Oyi4XAeFCQbJNBUzTHhZtV1VbplgfSUGBZN9gbyzg6ute3VatbgmeX8gahlfxnuEiAoqgOreubiwgKGNqFCnz+RCnWpvii0BI3mrsCurWO4gTyOGJ1JANxVewTSXV50C7ZHZYRcBSEOzWIPhQvUKgWFfAf/2oxh3QalmISwhk3GW2Lv78K1C18V3XgEEi4+EzjCyyJGToWH4fLObUo+cVFTyaPKRifDiNN0Sp0nlxtP81YoQfj/X55wwXY59n8Kzz6hTX9Z/P2ln1w/CLOxOmo1uRQAAAABJRU5ErkJggg==)
.
Собственные числа
![](data:image/png;base64,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)
матрицы монодромии называются мультипликаторами уравнения (4), а собственные числа
![](data:image/png;base64,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)
матрицы R — характеристическими показателями. Из определения R имеем
![](data:image/png;base64,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)
, при этом простым мультипликаторам соответствуют простые характеристические показатели, а кратным — характеристические показатели с элементарными делителями той же кратности.
Характеристические показатели определены с точностью до
![](data:image/png;base64,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)
. Из
![](data:image/png;base64,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)
и формулы Лиувилля следует, что
![](data:image/png;base64,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)
.
Название мультипликатор объясняется следующей теоремой:
Теорема. Число является мультипликатором уравнения (4) тогда и только тогда, когда существует ненулевое решение
![](data:image/png;base64,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)
этого уравнения такое, что при всех t
![](data:image/png;base64,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)
.
Следствие 1. Линейная периодическая система (4) имеет нетривиальное решение периода тогда и только тогда, когда по меньшей мере один из ее мультипликаторов равен единице.
Следствие 2. Мультипликатору
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC0AAAAVCAMAAADl7ZdoAAAAAXNSR0ICQMB9xQAAAF1QTFRFAAAAAQEBFBQvIiJOTyMjXTVMXjZNQEAnQ1h4Xn6XX3+YeFhDl35emH9fkHeEmay9pI6CvayZwc3YzsHB3OPm/v7++Pj3+Pn58vLv8fHu7vHx7/Ly9/j4+fn4////1xktpgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB6SURBVDjLxdNZDoAgDARQ6or7irve/5gSVGKIotUY5/s1NBlKJkzIJ5oxhK4CWt/WjUWkFq8wvc+kDj0+bZcPNNtyS0ewxFcmrzfZT77ZpD3Y5ESbXRWQvOg1VYZ0WHXqglFGkOjaAU6EHuMe8auuilG0g9G/X8MTPQNYh2T28yNI1gAAAABJRU5ErkJggg==)
соответствует так называемое антипериодическое решение
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAVCAMAAACJ68VtAAAAAXNSR0ICQMB9xQAAAFRQTFRFAAAAExMuLhMTPyY/IiJOTiIiTDVdXTVMQ1h4Xn6XeFhDaURpl35ekHeEmay9vayZr7fG2c7Cws7Z3+bf3OPm5uPc8vLv7/Ly+fn4+Pn55+zq////okqj9gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACySURBVCjPtZLrEoIgEEbXvERGECQI7fu/Z8CupNnUn2LGQTlw9hMA/Nzgx9yf51W346bjcddObzgvc9f0DPPCw9jdehARUarnWn1iHkYRjUIpoj9mIAHALgKgF63QHSxXJ4vvLXGTzImHUenCyZK4Yt7NxC1xnZOseBZlfzsVf/Lgxo+6mbTK04vZDfdL1tR8qQJQ5JLMQFPq1/8rH+ykaKut2vK6rVx9x7+dz9/vx2t7AGZePASy1ilrAAAAAElFTkSuQmCC)
периода , т. е.
![](data:image/png;base64,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)
. Отсюда имеем:
![](data:image/png;base64,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)
Таким образом,
![](data:image/png;base64,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)
есть периодическое решение с периодом
![](data:image/png;base64,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)
. Аналогично, если
![](data:image/png;base64,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)
(p и q — целые,
![](data:image/png;base64,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)
), то периодическая система имеет периодическое решение с периодом
![](data:image/png;base64,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)
.
Пусть
![](data:image/png;base64,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)
, где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAMAAADjcdz2AAAAAXNSR0ICQMB9xQAAAFRQTFRFAAAAAQEBExMuLhMTPyY/IiJOTiIiTyMjQ1h4Xn6XeFhDl35emay9vayZ2c7Cws7Z3OPm2+Ll5uPc/v7+7/Ly8vLv7vHx+Pj3+Pn5+fn48fHu////HT+f5gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPfc9JDoAgDAXQVgVlVgQn7n9PMWpoTKTLl/4OkD4FPzDnoqAAEATtUCxYcBREilwXiNwl3xKwbFnlsBUwAM/MG3apLQsEfDdeUwqYHFckclwLbTO9YBAxn9GjqD1XgROzqxhPYCHB7QAAAABJRU5ErkJggg==)
— матрица из теоремы Флоке,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAATCAMAAAB4HKeYAAAAAXNSR0ICQMB9xQAAAEtQTFRFAAAAAQEBExMuLhMTPyY/IiJOTyMjRFl5Q1h4Xn6XeFhDl35emay9vayZ2c7C3OPm5uPc5eLb/v7++Pn57/Ly+fn49/j48vLv////gtXnqAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABVSURBVCjPY5BABQzE8oWAAInPx8jAwC6MJC/AzIOino9VBIXPzYlinigXDwpfgIUfhc/LIQznCyGUg/ggpXxM/HA+L4eYIDMnwr3ibIyMPCT7DwcfAIHmGGzgxyecAAAAAElFTkSuQmCC)
— ее жорданова форма. По теореме Флоке
![](data:image/png;base64,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)
, или
![](data:image/png;base64,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)
, (5)
где
![](data:image/png;base64,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)
— фундаментальная матрица,
![](data:image/png;base64,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)
— -периодическая матрица. В структуре фундаментальной матрицы линейной системы с периодическими коэффициентами характеристические показатели играют ту же роль, что и собственные числа матрицы коэффициентов в структуре фундаментальной матрицы линейной системы с постоянными коэффициентами.
Пример. Рассмотрим дифференциальное уравнение второго порядка
![](data:image/png;base64,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)
, (6)
где
![](data:image/png;base64,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)
— -периодическая вещественная скалярная функция. Мультипликаторами уравнения (6) будем называть мультипликаторы соответствующей линейной системы, т. е. системы