Feigenbaum方程解的性質(zhì).pdf

1、華僑大學(xué)碩士學(xué)位論文Feigenbaum方程解的性質(zhì)姓名：蔡耀雄申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：陳爾明20050610Feigenbaum方程解的性質(zhì)AbstractIn70s，F(xiàn)eigenbaumfirstdiscoveredanastonishinguniversalmetricpropertyofperioddoublingbifurcationsinthetransitiontochaoticbehavior(ieth

2、eSO—calledFeigenbaumphenomenon)Forexplainingthisphenomenon，F(xiàn)eigenbaumproposedacertainnumberofassumptions，akeyodeofthemisthecmTespondingfunctionalequation如)一去92(一捌，(從(o，1)isf。dct枷ned)，(1)1／L、‘，【g(o)=1，一1sg(J)≤1，x∈【一1，1】，h

3、assolutionsManyscientistsineachfieldaleinterestedinthisequation，andtheyalsohaveobtainedrichfruitsinthisrespectIncludingFeigenbaumfunctionalequationhassolutions，theconstructionofmanykindsofcontinuous，differentiable，evensm

4、oothsolutions，andSOmedynamicalbehaviorsofFeigenbaummaps，andSOonConsideringsomerecentresultsoftheresearchonFeigenbaumfunctionalequation，first，weinvestigatetheconcavity—convexityofaclassofaccuratesolutionoftheFeigenbaumfun

5、ctionalequation，ThenweinvestigatethelikelylimitsetswitllfractalslamctureofsometypesofFeigenbaummapsinhighordercaseThefollowingaleourmainpoints：InChapter1，weintroduceSomeconcernedconceptsandresultsofdynamicalsystem，fracta

6、lgeometryandFeiganbaummapInChapter2，weinvestigatetheconcavity—convexityofaclassofaccuratesolutionoftheFeigenbaumfunctionalequationWeobtaintheresult：if烈砧bethefractionaldecreasingcontinuoussolutionofthesecondtypeofFeigenba

7、umfunctionalequation，whichhasbeenintroducedinreference【201，then“x)isconvexonkl】，andconcaveon[0，口](e(a)=0)tnChapter3，weinvestigatetheFeigenbaumfunctionalequationinhighordercaseandstudyaclassof29一order(q21)sin甜evalleyFeige