OQIM OPERATORLARI VA ULARNING XOSSALARI
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Abstract
Ushbu tezisda dinamik tizimlar nazariyasining muhim tushunchalaridan biri bo‘lgan oqim operatorlari va ularning asosiy matematik xossalari ko‘rib chiqiladi. Oqim tushunchasi, unga mos keluvchi evolyutsiya operatori, Koopman va Perron–Frobenius operatorlari ta’riflanadi. Operatorlarning yarim guruh xossasi, chiziqliligi, uzluksizligi, chegaralanganligi hamda infinitezimal generatori bilan bog‘liq xossalari tahlil qilinadi. Shuningdek, oqim operatorlari nazariyasining zamonaviy ma’lumotlarga asoslangan dinamik tizimlarni tahlil qilish usullaridagi ahamiyati ko‘rsatib o‘tiladi.
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