關于函數(shù)例外集的豪斯道夫維數(shù)---康托型函數(shù)、交錯跳躍函數(shù)及自相似函數(shù).pdf

1、華中師范大學碩士學位論文關于函數(shù)例外集的豪斯道夫維數(shù)康托型函數(shù)、交錯跳躍函數(shù)及自相似函數(shù)姓名：朱三國申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：李文俠19990501AbstractThispaperconsistsoftwopartsWeshalldiscusstheHausdorffdimensionofsetsofnon—differentlabilitypointsofsomeCantor—typefunctionsinthefi

2、rstpartandinthesec—ond，weconsidertheHausdorffdimensionoftheexceptionalsetsofalternativelyjumpingfunctionsandself—similarfunctionsInthefirstpartweshalldefinealocationcodeforeachpointinr0，1]，onthebasisofwhich，weshallgiveso

3、rrtepropertiesofCantor—typefunctions，Weconsidertheusualderivativewherewesaythederivativeexistsifthederivativelsfiniteor1nfiniteThesetsofthepointsatwhichthederivativedoesnotexistarecalledthesetsofnondifferentlabilicypoint

4、sNaturallywewillaskthefollowingtwoquestions1Howlargearethenon—differ—entiabilitysets2Canthenon—differentIabilitysetsbeignoredRichardDarst(E4])hasstudiedthesetsofnon“fferentiabilirypointsofCantorfunctions；theHausdorffdime

5、nsionhasbeengivenbyhimInthispaperweshallconsidertheCantor—typefunctionsandgivetheHausdorffdimensionandPackingdimensionofthesetsofnon—differentiblhypointsoftheCantor—typefunctionsAsweshahgee，themassdistri—butionprinciplet

6、ostudythelowerboundoftheHausdorffdimension([4])isinvalidinmypaper，andweshallusethedimensionaIresultsduetoFengDejuninsteadofthemassdistri—butionprincipleWhatIhavedonemthefirstpartcanbesummarisedasfollows(1)Weconsidertheho

7、mogeneousCantorsetCl=c([o，1]，2，(口”1)underthecon—dition∑m—o(M)andtheCantortypefunction(thedistributionfunctionoftheuniform^一1probabilitymeasure)；wegivetheHausdorffdimensionandpackingdimensionoftheserofnon—differentlabIlit

8、vpointsAsagenuinedimensionPackingdimensionisanimportantin—dextodescribeasetSothecalculationofthePackingdimensionisofsignificance(2)WeconsiderthepartialhomogeneousCantorsetC2：C(E0，1]，2，a1_‰))underthecondition∑d^一。(n)andth

9、eCantor—typefuncrion(thedistrIbutionfunetion。ftheuni—formprobabilitymeasure)；wegivetheHausdorffdimensionandpackingdimensionofthesetofnon—differentiabilitypoints，(3)Becauseoftheperturbationwe。made，themassdistributionprinc