Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Non-linear Dynamics
Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman
Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The basic question of this paper is: If you consider two iterated function systems close to one another in an appropriate topology, are the dimensions of their respective invariant sets close to one another? It is well-known that the Hausdorff dimension (and Lebesgue measure) of the invariant set do not depend continuously on the iterated function system. Our main result is that (with a restriction on the ‘non-conformality’ of the transformations) the Hausdorff dimension is a lower semi-continuous function in the C1- topology of the transformations of the iterated function system. The same question is raised of the …
On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang
On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang
Mathematics and Statistics Faculty Publications and Presentations
We classify all rational 2-reptiles in the plane. We also establish properties concerning rational reptiles in the plane in general.
Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman
Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upper- and and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the moduli of the eigenvalues of the underlying affine contraction are all equal (this includes Jordan blocks). The tiles we discuss play an important role in the theory of wavelets. We calculate the dimension for a …