P-АДИК РАЦИОНАЛЬНЫЕ ДИНАМИЧЕСКИЕ СИСТЕМЫ
Xамидов Шерали Ширинович Преподаватель Бухарского государственного педагогического института
Ключевые слова:
Рациональные динамические системы; фиксированная точка; инвариантное множество; Диск Зигеля; Множество p-адических комплексных чисел.Аннотация
В работе использованы методы математического анализа, комплексного анализа и p-адического анализа. Изучение теории динамических систем с дискретным временем в области p-адических комплексных чисел и их реализация:
• определить неподвижные точки a/(x^2+1) -рациональной функции;
• Реализация динамики, соответствующей характеристикам фиксированной точки, когда фиксированная точка единственно;
• найти периодические точки при отсутствии фиксированной точки и реализовывать динамику в соответствии с природой этих периодических точек.
Результаты работы по развитию теории дискретных динамических систем для класса p-адических рациональных функций, имеют практические применение в рассмотрения проблем телекоммуникаций и возможностью их использования в цифровом анализе и криптографии. Основные результаты имеют теоретический характер. Они используются в смежных областей математики и динамики биологических и физических систем.
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