Colloquium

Speaker: | Prof Jung-Chao Ban (National Dong Hwa University) |

Title: | HAUSDORFF AND MINKOWSKI DIMENSIONS OF SYMBOLIC SPACES UNDER (j,m)-DECIMATION |

Time: | 2013-10-31 (Thu.) 15:00 - 16:00 |

Place: | |

Abstract: | This talk considers the HausdorĀ§ and Minkowski di- mensions of symbolic spaces under ( j;m ) -decimation, where m is an integer and 1 j m . The problem is raised by Abram and Lagarias [W. Abram and J. C. Lagarias, p-adic path set fractals and arithmetic, arXiv:1210.2478, 2013.] on the study of the p -adic path set fractals and arithmetic in number theory. Four symbolic spaces, namely, subshift of Onite type, soOc shift, path set and p -path set fractal are considered herein. To compute their dimen- sions under ( j;m ) -decimation, we Orst establish their associated ( j;m ) -adjacency matrices. Such matrix is a rearrangement of the original one according to the pair ( j;m ) . Then we form a new la- beled graph by assigning suitable symbols on the edges of the graph induced from ( j;m ) -adjacency matrices. Finally, we proved that the Minkowski and HausdorĀ§ dimensions formula can be derived by the labeled ( j;m ) -adjacency matrices . On one hand, the result extends the classical results on the dimension formula of symbolic spaces; On the other hand, it be can applied to the p -adic path set fractals on number theory. |

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