Abstract
We extend Falconer’s formula from Falconer (Math. Proc. Camb. Philos. Soc. 103:339–350, 1988) by identifying the Hausdorff dimension of the limit sets of almost all contracting affine iterated function systems to the case of an infinite alphabet, non-autonomous choice of iterating matrices, and time-dependent random choice of translations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Falconer, K.: The Hausdorff dimension of self-affine fractals. Math. Proc. Camb. Philos. Soc. 103, 339–350 (1988)
Falconer, K.: The Geometry of Fractal Sets. Cambridge University Press, Cambridge (1990)
Jordan, T., Pollicott, M., Simon, K.: Hausdorff dimension for randomly perturbed self affine attractors. Commun. Math. Phys. 270, 519–544 (2007)
Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability. Cambridge Studies in Advanced Mathematics, vol. 44. Cambridge University Press, Cambridge (1995)
Rogers, C. A.: Hausdorff Measures, Cambridge University Press, Cambridge (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Urbański, M. (2014). Countable Alphabet Non-autonomous Self-affine Sets. In: Bandt, C., Barnsley, M., Devaney, R., Falconer, K., Kannan, V., Kumar P.B., V. (eds) Fractals, Wavelets, and their Applications. Springer Proceedings in Mathematics & Statistics, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-08105-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-08105-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08104-5
Online ISBN: 978-3-319-08105-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)