圖映射的等度連續(xù)性，吸引中心與拓撲熵.pdf

1、廣西大學(xué)碩士學(xué)位論文圖映射的等度連續(xù)性，吸引中心與拓撲熵姓名：張永平申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：孫太祥劉新和20050501廣西大學(xué)碩士學(xué)位論文圈映射的等度連續(xù)性，吸引中心與拓撲熵EQUICONTINUITY，THEATTRACTINGCENTERANDTHETOPOLOGICALENTROPYOFAGRAPHMAPABSTRACTDynanficalsystemgeneratedbygraphmapsstudymainl

2、ythetopologicalstruetliresoforbitsofgraphmapsInrecentyearsdynamicalpropertiesgeneratedbygraphniapshaveattractedextrenleattentionsincethereisaClOSeconnectionbetweendynamical1)eoDertiesofauto—homeomorphismsonsurfacesandtho

3、seofgraphmapsInthefieldofgraDhⅡlaps，onehasdonemanyresearchesandobtainedaseriesofremarkableresultsOurbasicobjectioninthispaperistostudytheequicontinuity，theattractingcenterandtiletopologicalentropyofgraphmapsInChapterOne，

4、weintroducesimplythedevelopmentaboutdynamicalsystemandthebackgroundofthispaper131Chaptel’Two，westudymainlytheequivalentconditionsofequicontinuityofgraphmapsForacontinuousgraphmapf，weshowthefollowiagfiveconditinonsareequi

5、valent：(1)，isequicontinuous；(2)thereexistsN∈Nsuchthatf“isuniformly(10n—vergent；(3)，isSequicontinuousforsomesubsequenceS=n1：n2，)ofN：(4)r2(2，)=u(茁，f)foranyz∈G：(5)盯：l!mx，，)—呻limx，)isaperiodicmapInChapterThreewediscussmainly

6、theconnectionsaboutunilateral1一limitpointsspecial。一limitpointsandtheattractingcenterofacontinuousgraphmapfWeshowthat(1)z∈scdy，f)(forsome9∈G)ifandonlyifX∈sa(x，，)；(2)Ar(f)uP(f)[Usn(Ⅳ，)：(3)AP(f)uP(f)=u(f2(，))=aj(co(f))一u(U—

7、sa(y：，))=w(AI、(，)u∈【jⅣeuP(，))Furthermore，wealsoobtainseveralequivalentconditionsaboutfwhichhaspos—itivetopologicalentropy：(1)h(f)o；(2)可萬一R(f)isuncountable；(3)n(，)一只(，)isanuncountableset；(4)thereexistsz隹n(f)suchthatz=P(x，