Title
Nebesnaya mekhanika na sfere i v prostranstve Lobachevskogo: Bifurkatsionnyy i topologicheskiy analiz obobshcheniy zadach Kepler,Used
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Predlagaemaya monografiya ob"edinyaet naibolee interesnuyu oblast' znaniy, nebesnuyu mekhaniku, s sovremennymi geometricheskimi metodami issledovaniya. Poskol'ku gravitatsionnyy potentsial imeet osobennost' (chto sootvetstvuet padeniyu material'noy chastitsy na tsentr), issleduemye sistemy, zadachi Keplera, Eylera i Lagranzha, formal'no govorya, ne yavlyayutsya integriruemymi po Liuvillyu (vektornoe pole, porozhdaemoe gamil'tonianom, ne yavlyaetsya polnym). V rabote opisana regulyarizatsiya, posle kotoroy vektornoe pole stanovitsya polnym i vedet sebya regulyarnym (integriruemym) obrazom. Rassmatrivaemye zadachi yavlyayutsya estestvennymi obobshcheniyami klassicheskikh ploskikh zadach nebesnoy mekhaniki. V monografii postroeny bifurkatsionnye diagrammy, proveden topologicheskiy analiz, vypolnena klassifikatsiya oblastey vozmozhnosti dvizheniya na konfiguratsionnom prostranstve (opisany vse tipy dvizheniy: regulyarnye i predel'nye dvizheniya), pokazana svyaz' integriruemykh zadach nebesnoy mekhaniki v prostranstvakh postoyannoy krivizny.
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