復動力系統(tǒng)中的非一致雙曲性假設及其Julia集的分形維數(shù).pdf

1、中國科學技術大學博士學位論文復動力系統(tǒng)中的非一致雙曲性假設及其Julia集的分形維數(shù)姓名：李懷彬申請學位級別：博士專業(yè)：基礎數(shù)學指導教師：沈維孝20100401ABSTRACTABSTRACTThethesisconsistsoftwotopicsofnon—uniformhyperbolicityassumptionsanddimensionsofJuliasetsincomplexdynamicsInthefirstpart，weg

2、iveessentiallyequivalentformulationsofthebackwardcontractingpropertydefinedbyJuanRiveraLetelier，intermsofexpansionalongtheorbitsofcriticalvaluesInthesecondpart，Westudytherelationsoffractaldimensions，byinvestigatingthepro

3、pertiesofconformalmeasuresontheJuliasetThethesisisorganizedasfollows：Inchapter1，webrieflyrecalltheofgin，developmentsandmainobjectiveincomplexdynamics，andthenweintroducethebackgroundsandmainresultsofthethesisInchapter2，we

4、reviewsomepreliminarynotionsandresultsincomplexanalysisandcomplexdynamics，whichwillbeusedinourthesisInchapter3，wefirstdescribeaYoccozpuzzlepartition，bymakinguseofequipo。tentialcurvesfortheGreenfunctionandallboundedperiod

5、icFatoucomponents，ex。ternalraysandinternalrays，andthenwegivethepreciseformofcomplexboundstheoremInchapter4，wegiveessentiallyequivalentformulationofthebackwardcontractingpropertydefinedbyJuanRivera—Letelierintermsofexpans

6、ionalongtheorbitsofcriticalvalues，forcomplexpolynomialsofdegreeatleast2whichareatmostfinitelyrenormalizableandhaveonlyhyperbolicperiodicpointsInchapter5，weprovethatarationalmap廠ofdegreeatleast2whichhasnoparabolicpointsan

7、dJ(，)≠一C，satisfiesthesummabilityconditionwithexponent∥∈(0，1】ifandonlyifthereexist600andafunctionr：(0，釉_(1，。。)suchthat廠isbackwardcontractingwithgrowthfunctionr(d)and一㈣一p譬ooInchapter6，weshowthattheupperboxdimensionoftheJul