QAYTISH VAQTIGA DOIR FUNDAMENTAL TEOREMALAR
;
qaytish vaqti, ergodiklik, Markov jarayonlari, Poincare teoremasi, Kac formulasi, ehtimollar nazariyasi, topologik dinamik tizim, invariant o‘lchov, stoxastik jarayon.Abstrak
Mazkur maqolada ehtimollar nazariyasi va topologik dinamik tizimlar doirasida qaytish vaqti tushunchasi hamda unga oid fundamental teoremalar yoritilgan. Ayniqsa, Poincare qaytish teoremasi va Kac teoremasi asosida tasodifiy va deterministik tizimlarda obyektlarning o‘z boshlang‘ich holatiga qaytish ehtimoli, vaqti va shartlari matematik jihatdan izohlanadi. Ushbu natijalar ergodik nazariya, Markov jarayonlari, fizik modellar va kompyuter simulyatsiyalarida keng qo‘llaniladi. Maqolada ushbu teoremalar formulalari, izohli misollar va ularning qo‘llanilishi bo‘yicha tahlillar keltirilgan.
Iqtiboslar
Qodirov, Farrux. "On the properties of homeomorphisms of the circle with singularities." Uzbek Mathematical Journal, vol. 2020, no. 2, 2020, pp. 45–53.
Qodirov, Farrux, and B. Aliev. "Invariant sets of circle homeomorphisms with singular points." Bulletin of Tashkent University, vol. 2021, no. 1, 2021, pp. 34–42.
Qodirov, Farrux. "Dynamical systems and the behavior of circle mappings under continuous transformations." International Journal of Mathematical Sciences, vol. 17, no. 4, 2022, pp. 101–110.
Qodirov, Farrux. "Topological aspects of circle transformations in one-dimensional manifolds." Scientific Reports of Mathematics Department, vol. 9, no. 3, 2021, pp. 22–30.
Qodirov, Farrux. "Homeomorphisms and their fixed points on compact topological spaces." Journal of Applied Topology and Geometry, vol. 8, no. 2, 2023, pp. 88–97.
Qodirov, F. E., O. D. Doniyorov, and H. Shokirov Sh. "Basic concepts of information security in information systems. Wide threats and their consequences." концепции устойчивого развития науки в современных условиях (2021): 153-155.
Bozorova, Irina Jumanazarovna, and Dilfuzaxon Mamasharipovna Karayeva. "Modern programming technologies and their role." интеллектуальный капитал xxi века. 2020.
Ergash o’g’li, Qodirov Farrux. "Hududlarni ijtimoiy-iqtisodiy rivojlantirishda har bir hududning о ‘ziga xos xususiyatlari." Scientific Journal of Actuarial Finance and Accounting 4.09 (2024): 178-183.
Qodirov, Farrux, and Zuhriddin Mardonov. "BLOKCHEYN TEXNOLOGIYASI VA UNING QO’LLANILISHI." Наука и технология в современном мире 4.6 (2025): 27-32.
Qodirov, F. E. "Methodological aspects and importance of development of medical services through econometric modeling and forecasting options." academy. uz/index. php/yo.
Qodirov, Farrux, and Sabrina Turayeva. "ELEKTRON TIJORAT PLATFORMALARINING EKOLOGIK TOZA QISHLOQ MAHSULOTLARI BOZORIGA TA’SIRI." Наука и технология в современном мире 4.7 (2025): 37-44.
Qodirov, Farrux, and Sabrina Turayeva. "BULUTLI HISOBLASH TEXNOLOGIYALARI VA AI ASOSIDA QISHLOQ XO ‘JALIGIDA PROGNOZLASH TIZIMLARI." Наука и технология в современном мире 4.7 (2025): 45-52.
Qodirov, Farrux, and Sabrina Turayeva. "AQLLI SHAHAR (SMART CITY) TIZIMLARI ORQALI EKOLOGIK MONITORING VA RESURSLARNI TEJASH." Наука и технология в современном мире 4.7 (2025): 21-28.
Qodirov, Farrux, and Sabrina Turayeva. "IOT TEXNOLOGIYALARIDAN FOYDALANIB CHIQINDILARNI AVTOMATLASHTIRILGAN BOSHQARISH TIZIMLARI." Наука и инновация 3.10 (2025): 68-75.
Qodirov, Farrux, and Sabrina Turayeva. "GEOGRAFIK AXBOROT TIZIMLARI (GIS) ASOSIDA YER VA SUV RESURSLARINI MONITORING QILISH." Инновационные исследования в современном мире: теория и практика 4.10 (2025): 85-91.
