25584.palmer線性化定理的改進

1、Palmer線性化定理的改進onthelinearizationtheoremofPalmerntheeoremoU作者：王蓉婷Author：W————a——ngRongting指導教師o夏永輝專學業(yè)：應用數(shù)學Supervisor：墨i壘!囟望g塾堅iMajor：位：理學碩士Degree：授予單位：浙江師范大學MasterofScienceInstitute：圣墜盤i壘望g盟Q!!墜壘!旦望i翌!璺i主YMarch，2014Abstra

2、ctThepurposeofthispaperistostudynonautonomousdifferentialequationslin—earizationtheorem，respectivelyfromtwoaspectstoimproveandgeneralizethePalmerlinearizationtheoremOnonehand，weweakentheassumptionofLipschitziancondi—tion

3、inthePalmerlinearizationtheorem；Ontheotherhand，weweakentheassumptionthatnonlineartermisboundedMoreover，weprovethatthetopologicallyequivalentfunctionsareH61dercontinousThisessayisdividedintothreechaptersInchapter1，webrief

4、lyintroducetheresearchbackground，motivation，andnoveltySomedefinitionsandlemmasarealsointroducedinthischapterInchapter2，weprovethatsystem三!三AA。l。(。t，)zx。1，(￡’z1，z2)’istopologicallyconjugatedtosystem(5)Usingthetheoryofexpo

5、nentialdichotomyweconstructtopologicalhomeomorphismfunctionbetweennonlinearsystem(5)andlinearsystem(6)Moreover，weprovethatthehomeomorphismfunctionsareH61dercontinousWereduceLipschitzianconditiontolocalintegrablefunctionT

6、herefore，weimprovethePalmerlinearizationtheoremInchapter3，ifthenonlineartermisunbounded，weprovethatthefollowsystemA(t)xf(t，z)，B(t)y妒(t：X)矽(￡，Y)istopologicallyconjugatedtosystemV7=A(t)v，札7=B(t)uBytheexistenceanduniqueness