一类自相似集hausdorff测度的计算

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1、Æ“è10530ÆÒ201510111135©aÒO184—?a¬ÆØ©˜agƒq8HausdorffÿÝOŽÆž<ÛŸ•P“¸I‘BÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••©/AÛ9ÙA^"˜lcÊ›ÊF˜agƒq8HausdorffÿÝOŽÆž<ÛŸ“6¶9…¡¸I‘BÇƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••©/AÛ9ÙA^Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2018–5–25CalculationofHausdormeasureforaclassofself-similarsetCandidateHu

2、iLuoSupervisorAssociateProfessorGuoshengHanCollegeSchoolofMathematicsandComputationalScienceProgramMathematicsSpecializationFractalGeometryandItsApplicationDegreeMasterofScienceUniversityXiangtanUniversityDateMay25th,2018Á‡©/AÛ´20•V70c“uÐå5˜€#Ɖ§Ì‡ïÄé–´Ø5KAÛã/§~XÛ/%G秩fÃ5K$Ä

3、;,§‡ð•ò°W‚"§gŽÚ•{®²'߈‡Æ‰ƒ¥§=¦©/AÛù€Æ‰k2•A^§´ÒnØïÄ¿Ø´AON´§cÙ´©/8Hausdorff‘êÚÿÝOŽ§¦+´gƒq8§HausdorffÿÝOŽ•´AO(J"©Ì‡?ز¡þ˜agƒq8SÚn‘˜m˜agƒq8WHausdorffÿÝOŽ"©o
©•oÙ"1˜ÙµØㆩk'µ9©/yG"1Ùµé©/8Ľ±9ƒ'ÚnŠ•[Qã"1nÙµÄk3²¡þE˜agƒq8S§,éS?1þe.O§SHausdorffÿÝpO(Š§=H1(S)

4、=2§Óž„˜‡íاƒq'•1(0<1<1)…rr5log3ps=log3+5ž§Hs(S)=(2)s§Ù¥s•Hausdorff‘ê"1oÙµ•r1logrÄ3üá•NS)¤˜agƒq8W§©O

5、^g,CXnÚŸþ©Ùpppnþ.•3Úe.•3§lH1(W)=3"'…cµgƒq8;HausdorÿÝ;Hausdor‘ê;g,CX;Ÿþ©ÙIABSTRACTFractalgeometryisanewdisciplinedevelopedinthe1970s,Themainresearchobjectareirregulargeomet

6、ricfigures,Suchasgrotesqueclouds,molecularmovementofthetrackwithoutrules,Meanderingcoastlineandmore.Anditsideasandmethodshaveinfiltratedintovariousdisciplines,evenifthefractalgeometryhasawiderangeofapplications.However,itsowntheoryresearchisnotparticularlyeasy.especiallyforthecomput

7、ationofthefractalsetHausdordimensionandmeasure,Inspiteoftheself-similarset,thecalculationoftheHausdormeasureisalsoparticularlydicult.ThispapermainlydiscussesthecalculationoftheHausdormeasureofaclassofself-similarsetSinaplaneandaself-similarsetWinthree-dimensionalspace.Thefulltext

8、isdividedintofourchapters.Thefirstchapterdiscussestheback-groundofthisarticleandthecurrentstatusoffractalgeometry.Thesecondchaptergivesadetaileddescriptionofthebasicdefinitionsoffractalsetsandrelatedlem-mas.Inthethirdchapter,aclassofself-similarsetsSisfirstconstructedintheplane,thent

9、heupperandlowerboundsofSareestima