二次系統(tǒng)極限環(huán)的有限性問題.pdf

1、安徽大學(xué)碩士學(xué)位論文二次系統(tǒng)極限環(huán)的有限性問題姓名：胡琴申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：盛立人2003.5.1室苧苧蘭塑主蘭竺蘭絲查一AbstractInthispaperwewillprovethatquadraticsystemhasatmostfinitelylimitcyclesBamonclaimedthathehadfinishedthedemonstrationofthefinitenessof1imitcycl

2、es，butheused11’yashenkoTheorem，whichinvolvessomeknowledgeofcomplexdomain，SOitisthemainideatogive11’yashenkoTheoremallelementaryproofinthispaperWhatwehavedoneinthispaperistoprovethatunboundedpolycycleofquadraticsystemisfi

3、nite，whichinvolvestheCaseofunboundedhyperbolicpolycyclesandthecaseofunboundednonhyperbolicpolycyclesThemainpartisthefirstcase，thatistosayitisthe11yashenkoTheoremTogetoarrcsuttweaa。pttwoeq腳tnes等=筆；eana導(dǎo)=專i=g，where捌anasare

4、theeigenvaluesofthesingularpointstothelinearpartsIthasbeenproventhatthesystemhasfinitelimitcycleswhentheequalitiesdonotexist，SOweneedtostudytheothercaseUnderthisconditionwemuststudythepossibleexistenceofseparatrixcyclesa

5、ndtheaccumulationoflimitcyclesaccordingtodifferentclassificationsofkandgThemostkeycasehappenswhenkandgbelongto(一o。，0)HereareonlyhyperbolicsaddlesintheseparatrixcycleWhethertheequalitiesexistdecideswhetherthecyclecailcons

6、istsimplegraphornotThenweconsiderthecasewhenthoseseparatrixcyclesconsistsimplegraphs，thatistosay，theycanmaketheequalitiesexistDuringtheillustration，weusesometheoremsaboutthenon—existenceandtheuniquenessoflimitcyclesAtthe