| ON THE STRUCTURE OF THEATTRACTORS OF HYPERBOLICITERATED FUNCTION SYSTEM |
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| 作者姓名： | 殷庆和 |
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| 作者单位： | Department Of Mathematics，China University of Geosciences，Wuhan 430074，China |
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| 摘 要： | 1.IntroductionThefractalsgeneratedbytheattractorsofiteratedfunctionsystems(i.f.s.)havebeenresearchedbymanyauthorsfl--3'6'7'9].ByaniteratedfunctionsystemwemeanacompactmetricspaceXtogetherwithacollectionofcontinuousmapsTI,T2,'tTNonit,denotedby(X,TI,',TN).IfalltheTi'sarecontractionswecall(X;TI,',TN)ahyperboliciteratedfunctionsystem(h.i.f.s.).NForanh.i.f.s.thereexistsacompactsubsetAofX,suchthatA=.UTi(A).Aiscalledtheattractoroftheh.i.f.s.DenoteZ=(1,2,',N)N,anddefineametricdonZby…
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| 收稿时间： | 17 October 1994 |
On the structure of the attractors of hyperbolic iterated function systems |
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| Yin Qinghe.ON THE STRUCTURE OF THEATTRACTORS OF HYPERBOLICITERATED FUNCTION SYSTEM[J].Acta Mathematicae Applicatae Sinica,1998,14(2):152-156. |
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| Authors: | Yin Qinghe |
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| Institution: | (1) Department of Mathematics, China University of Geosciences, 430074 Wuhan, China;(2) Present address: Department of Pure Mathematics, the University of Adelaide, 5005 Adelaide, SA, Australia |
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| Abstract: | In this paper, we discuss the construction of attractors and Markov attractors of hyperbolic iterated function systems. We
show that whenM is an irreducible 0–1 matrix, for a huge amount (in the sense a.e. for any ergodic measure) of elements (j
1,j
2,...)∈Σ
M
the Markov attractorA
M can be approached by the set {T
jkoT
jk−1o...oT
jl
x; k≥m} ∀x∈X |
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| Keywords: | Markov attractors |
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