Andrey Opimakh Uravneniya Laksa: Deformiruyushchie kommutiruyushchie napravleniya v prostranstve Z na Z matrits - internet üzerinden indir

Uravneniya Laksa: Deformiruyushchie kommutiruyushchie napravleniya v prostranstve Z na Z matrits

Matematik

Dannaya rabota nachinaetsya s osnovnogo mnozhestva kommutiruyushchikh napravleniy v prostranstve Z na Z matrits, kotorye yavlyayutsya generatorami gruppy kommutiruyushchikh potokov. Glavnaya chast' v etoy rabote sostoit iz deformatsiy etikh napravleniy otnositel'no parametrov etikh potokov i ikh uravneniy. Kombinatsiya evolyutsiy vozmushchennykh matrits otnositel'no vsekh napravleniy privodit k tak nazyvaemym ierarkhiyam nelineynykh differentsial'nykh i raznostnykh uravneniy. Spetsial'nye primery etikh uravneniy, poluchennykh v rabote, yavlyayutsya uravneniyami udovletvoryayushchimi beskonechnoy reshetke Tody. Zdes' issleduyutsya tri tipa deformatsiy: vo-pervykh, deformatsii osnovnykh napravleniy v nizhnetreugol'nykh matritsakh, s glavnym chlenom ravnym osnovnomu napravleniyu. Vo-vtorykh, deformatsii v verkhnetreugol'nykh matritsakh s sokhraneniem glavnogo chlena. V tret'em sluchae rassmatrivayutsya kombinatsii napravleniy pervogo i vtorogo tipa. Vo vsekh etikh trekh tipakh opisyvaetsya algebraicheskaya struktura uravneniy i pokazyvaetsya ekvivalentnost' razlichnykh form, v kotorykh oni poyavlyayutsya. Odna iz nikh, forma nulevoy krivizny, svyazannaya s beskonechnomernoy zadachey Koshi. V rabote pokazyvaem edinstvennost' resheniya etoy zadachi Koshi.

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