Робота присвячена дослідженню динамічних систем з точковими атракторами рекурентним методом перетворення дискрентнимх даних із множини натуральних чисел, в напрямку зростання степеня двійки (пряма задача Якобсталя) і у зворотному напрямку (реверсна задача Коллатца). Вперше висловлена і ідея розшарування перетворенням чисел Якобсталя множини ℕ на окремі підмножини, що не перекриваються. Встановлено, що даний ефект корелює із закономірностями послідовностей типу Коллатца в реверсному напрямку перетворення множини ℕ початкових чисел. Показано, що кількість груп сегрегації множини ℕ корелює із числом періодичних циклів завершення послідовностей Коллатца, плюс група чисел, що формує безмежно зростаючі послідовності Коллатца.
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