廣義Hamilton系統(tǒng)規(guī)范型進(jìn)一步研究.pdf

1、廣義Hamilton系統(tǒng)規(guī)范型進(jìn)一步研究FurtherStudiesOilthenormalformofgeneralizedHamiltoniansystems作者：李志清Author：圣塾iQi壘受曼i指導(dǎo)教師：壑堂堡Supervisor：——Xia—oHuaZ—h—ao專業(yè)：應(yīng)用數(shù)學(xué)學(xué)O：墨堂塑Degree：叢箜圭旦!望￡曼竺i旦望塑授予單位：浙江師范大學(xué)Institute：—、ZhejiangNormalUniversity——

2、May2016AbstractAgeneralizedHamiltoniansystemdefinedonPoissonmanifoldisageneralizationofaclassicalHamiltoniansystemdefinedonsymplecticmanifoldwithevendimension，whilemaintainingthemostpropertiesofclassicalHamiltoniansystem

3、sTheycanbeusedtodescribebroaderdynamicalmodel，andhavebeenusedinawiderangeofapplications，suchasmathematicalphysics，biologyaerospaceandotherfieldsNormalformtheoryisoneofpowerfultoolsforresearchinglocMbifurcationofnonlinear

4、dynamicsystem，andhasalonghistoryFortheclassicalHamiltoniansystemthroughavarietyofsylnplectictransformationmethod，thereductionproblemofHamil—toniansystemscanbeconvertedtothereductionofHamiltonianfunctionsThisisaveryimport

5、antfieldofdynamicalsystems，andhasalonghistoryandabundantresearchresultsInthispaper，basedonthefactthattheflowdefinedbygeneralizedHamiltoniansystemisaone—parametricstructurepreservingnonlineartransformationandsomepre—vious

6、relatedworks，wefurtherstudythenormMformofgeneralizedHamiltoniansystemwithLiePoissonstructure，andobtainthegenerMtheoreticalcalculationmethodInaddition，thetheoreticalmethodsareusedtostudyakindofgeneralizedHamiltoniansystem

7、sdefinedontheLiealgebradualspace(so(3))’，obtainthenormalformofthesesystemsuptothirdorder，thecorrespondingthirdordertruncatednormalformsystemisageneralizedHamiltoniansystemwiththreeparametersFinallybasedonthefoliationstru

8、ctureofphasespaceforgeneralizedHamiltonsystemandthenatureoftheHamiltonfunction，wecarefullyanalysethephaseportraitofthethirdordertruncationsystembyusingbifurcationtheoryandobtainallpossibledistributionsoftheirphaseorbitsK