測(cè)度空間上的拓?fù)湫蛄徐?pdf

1、中國(guó)科學(xué)技術(shù)大學(xué)碩士學(xué)位論文測(cè)度空間上的拓?fù)湫蛄徐匦彰汉瓷暾?qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：葉向東20070501AbstractInthisarticle，wemainlydiscuSSthepropertiesoftopologicalentropyandtopologicalsequenceentropyofTDSParticularly8sfortopouullsystemwhetherthereareanyrelat

2、ionshipbetween(X，T)and(M(x)，T)Weintroducethetopologicalsequenceentropyofagivenpseudometricspaceequippedwithaselfmapandstudyitforaspecialclassofpseudometricsinducedbycontinuousrealvaluedfunctionsonthespace，Asallapplicatio

3、n，weprovethatifXiszerodimensionaland4￡Zi8agivensequencethen僻，T)haszerotopologicalentropyalong4ifandonlyif(M僻)，T)haszerotopologicalentropyalongAInparticular，ifxi8zemdiraensionalthen(X，T)istoponuUifandonlyif(朋(x)，Di8toponu

4、llThepaperi8organizedasfollows：InthefirstchapterpreliminariesontopologicaldynamicalsystemarerecommendedInthesecondchapterwediscussthebasicpropertiesconcerninginvariantandentropyInthethirdchapter，westarttostudytherelation

5、shipbetween(x，T)and(M僻)，研Firstweintroducethetopologicalsequenceentropyofagivenpseudometricspaceequippedwithaselfmap，thenconsiderthetopologicalsequenceentropyforaspecialclassofpseudometricsinducedbycontinuousrealvaluedfun

6、ctionsOilthespaceWeprovethatforanyTDSandagivensequenceA￡z，(X，T)haszerotopologicalentropyalong一4ifandonlyifpseudometricsinducedbycontinuousrealvaluedfunctionsonthespacehavezerotopologicalentropyalong4Inadditionweprovethat