Hausdorff Dimension in Graph Directed Constructions
Open Access
- 1 October 1988
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 309 (2) , 811-829
- https://doi.org/10.2307/2000940
Abstract
We introduce the notion of geometric constructions in governed by a directed graph and by similarity ratios which are labelled with the edges of this graph. For each such construction, we calculate a number which is the Hausdorff dimension of the object constructed from a realization of the construction. The measure of the object with respect to is always positive and -finite. Whether the -measure of the object is finite depends on the order structure of the strongly connected components of . Some applications are given.Keywords
This publication has 9 references indexed in Scilit:
- Hausdorff measures, by C. A. Rogers. Pp. xxx + 195. £17.95. 1998. ISBN 0 521 62491 6 (Cambridge University Press).The Mathematical Gazette, 1999
- Hausdorff dimension and Perron-Frobenius theoryIllinois Journal of Mathematics, 1989
- Dimension and Dynamics for Fractal Recurrent SetsJournal of the London Mathematical Society, 1986
- The Geometry of Fractal SetsPublished by Cambridge University Press (CUP) ,1985
- Entropy, Large Deviations, and Statistical MechanicsPublished by Springer Nature ,1985
- Mesures de Hausdorff et théorie de Perron-Frobenius des matrices non-négativesAnnales de l'institut Fourier, 1985
- An Introduction to Ergodic TheoryPublished by Springer Nature ,1982
- Billingsley Dimension in Probability SpacesPublished by Springer Nature ,1981
- Additive functions of intervals and Hausdorff measureMathematical Proceedings of the Cambridge Philosophical Society, 1946