Contraction ratios for graphdirected iterated constructions
Author:
Manav Das
Journal:
Proc. Amer. Math. Soc. 134 (2006), 435442
MSC (2000):
Primary 28A78, 28A80
Published electronically:
June 14, 2005
MathSciNet review:
2176012
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We provide necessary and sufficient conditions for a graphdirected iterated function system to be strictly contracting.
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 M. Das, Hausdorff measures, dimensions and mutual singularity, Trans. Amer. Math. Soc., (to appear).
 2.
 M. Das and G. A. Edgar, Separation properties for graphdirected selfsimilar fractals, Topology Appl., (to appear).
 3.
 M. Das and G. A. Edgar, (preprint). Weak separation in graphdirected selfsimilar fractals.
 4.
 M. Das and S.M. Ngai, Graphdirected iterated function systems with overlaps, Indiana Univ. Math. J. 53 (2004), 109134. MR 2048186
 5.
 G. A. Edgar, Measure, topology, and fractal geometry, SpringerVerlag, New York, 1990. MR 1065392 (92a:54001)
 6.
 G. A. Edgar and Jeffrey Golds, A fractal dimension estimate for a graphdirected iterated function system of nonsimilarities, Indiana Univ. Math. J. 48 (1999), no. 2, 429447. MR 1722803 (2001b:28012)
 7.
 G. A. Edgar and R. D. Mauldin, Multifractal decompositions of digraph recursive fractals, Proc. London Math. Soc. 65 (1992), 604628. MR 1182103 (93h:28010)
 8.
 K. J. Falconer, Techniques in fractal geometry. John Wiley & Sons, Ltd., Chichester, 1997. MR 1449135 (99f:28013)
 9.
 K. J. Falconer, Fractal geometry. Mathematical foundations and applications, John Wiley & Sons, Ltd., Chichester, 1990. MR 1102677 (92j:28008)
 10.
 J. E. Hutchinson, Fractals and selfsimilarity, Indiana Univ. Math. J. 30 (1981), 713747. MR 0625600 (82h:49026)
 11.
 Fritz v. Haeseler, HeinzOtto Peitgen and Gencho Skordev, Global analysis of selfsimilarity features of cellular automata: selected examples, Phys. D 86 (1995), no. 12, 6480. MR 1353952 (97b:58075)
 12.
 Su Hua and Hui Rao, Graphdirected structures of selfsimilar sets with overlaps, Chinese Ann. Math. Ser. B 21 (2000), no. 4, 403412. MR 1801772 (2003g:11087)
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 I. N. Herstein and David J. Winter, Matrix theory and linear algebra. Macmillan Publishing Company, New York, 1988. MR 0999134 (90h:15001)
 14.
 K.S. Lau, J. Wang and C.H. Chu, Vectorvalued ChoquetDeny theorem, renewal equation and selfsimilar measures, Studia Math. 117 (1995), 128. MR 1367690 (97m:43001)
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 M. McClure, DirectedGraph Iterated Function Systems, Mathematica in Education and Research, (to appear).
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 Mark McClure, The Hausdorff dimension of Hilbert's coordinate functions, Real Anal. Exchange 24 (1998/99), no. 2, 875883. MR 1704763 (2000h:26013)
 17.
 R. D. Mauldin and S. C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc., 309, (1988), 811829. MR 0961615 (89i:28003)
 18.
 Lars Olsen, Random Geometrically Graph Directed SelfSimilar Multifractals, Pitman Research Notes in Mathematics Series, Vol. 307, Longman Scientific and Technical, 1994. MR 1297123 (95j:28006)
 19.
 R. S. Strichartz, Selfsimilar measures and their Fourier transforms III, Indiana Univ. Math. J., 42, (1993), 367411. MR 1237052 (94j:42025)
 20.
 JingLing Wang, The open set conditions for graph directed selfsimilar sets, Random Comput. Dynam., 5, (1997), no. 4, 283305. MR 1483871 (99g:28019)
 21.
 Hui Xu, The Hausdorff dimension and measure of conformal graphdirected sets, (Chinese) Acta Math. Sinica, 44, (2001), no. 4, 633640. MR 1850164 (2002h:28008)
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Additional Information
Manav Das
Affiliation:
Department of Mathematics, 328 Natural Sciences Building, University of Louisville, Louisville, Kentucky 40292
DOI:
http://dx.doi.org/10.1090/S0002993905081463
PII:
S 00029939(05)081463
Keywords:
Directed graphs,
graphdirected iterated function systems,
selfsimilar
Received by editor(s):
September 13, 2004
Published electronically:
June 14, 2005
Communicated by:
Michael Handel
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
