Separation properties for MW-fractals

Li Wenxia

doi:10.1007/BF02580406

Separation properties for MW-fractals

Li Wenxia

Central China Normal University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Corresponding to the irreducible 0 -1 matrix (a_ij)_nxn, take simultude contraction mappings φ_ij for each a_ij = 1, in R^d with ratio 0 < rtj < 1. There are unique nonempty compact sets F₁ , ⋯, F_n satisfying for each 1 < i < n, F_i = Uⁿ>=i φ_ij(F_j). We prove that open set condition holds if and only if Fi is an s-set for some 1 < i < n, where s is such that the spectral radius of matrix (r) is 1.

Original language	English
Pages (from-to)	487-494
Number of pages	8
Journal	Acta Mathematica Sinica
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/BF02580406
State	Published - 1998
Externally published	Yes

Keywords

A/W-fractal
Open set conditions
S-set

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10.1007/BF02580406

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abstract = "Corresponding to the irreducible 0 -1 matrix (aij)nxn, take simultude contraction mappings φij for each aij = 1, in Rd with ratio 0 < rtj < 1. There are unique nonempty compact sets F1 , ⋯, Fn satisfying for each 1 < i < n, Fi = Un>=i φij(Fj). We prove that open set condition holds if and only if Fi is an s-set for some 1 < i < n, where s is such that the spectral radius of matrix (r) is 1.",

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year = "1998",

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AU - Wenxia, Li

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N2 - Corresponding to the irreducible 0 -1 matrix (aij)nxn, take simultude contraction mappings φij for each aij = 1, in Rd with ratio 0 < rtj < 1. There are unique nonempty compact sets F1 , ⋯, Fn satisfying for each 1 < i < n, Fi = Un>=i φij(Fj). We prove that open set condition holds if and only if Fi is an s-set for some 1 < i < n, where s is such that the spectral radius of matrix (r) is 1.

AB - Corresponding to the irreducible 0 -1 matrix (aij)nxn, take simultude contraction mappings φij for each aij = 1, in Rd with ratio 0 < rtj < 1. There are unique nonempty compact sets F1 , ⋯, Fn satisfying for each 1 < i < n, Fi = Un>=i φij(Fj). We prove that open set condition holds if and only if Fi is an s-set for some 1 < i < n, where s is such that the spectral radius of matrix (r) is 1.

KW - A/W-fractal

KW - Open set conditions

KW - S-set

UR - https://www.scopus.com/pages/publications/3042948365

U2 - 10.1007/BF02580406

DO - 10.1007/BF02580406

M3 - 文章

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SN - 1000-9574

VL - 14

SP - 487

EP - 494

JO - Acta Mathematica Sinica

JF - Acta Mathematica Sinica

IS - 4

ER -

Separation properties for MW-fractals

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Keywords

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