臺灣博碩士論文加值系統

本篇論文研究矩陣值勢能在sofic shift 空間上相對應的平衡測度。用本篇論文所造出來的平衡測度，可以得到在sofic shift 空間上維度的譜分析的結果。最重要的是，我們提供一個在sofic shift 空間上，測度$
u$是嚴格的sofic 測度的例子。

This thesis studies equilibrium measures that correspond to the matrix-valued potential on a sofic shift space. With the construction, the analysis
of dimension spectrum is then available. Most important of all, there is an example shows that $
u$ is a strict sofic measure.

中文摘要………………………………………………………………i
英文摘要………………………………………………………………ii
誌謝……………………………………………………………………iii
Contents………………………………………………………………iv
1 Introduction………………………………………………………1
2 Backgrounds ………………………………………………………2
3 Main Theorem………………………………………………………3
4 Examples……………………………………………………………10
References……………………………………………………………18

[1] D. J. Feng. Lyapunov exponents for products of matrices and multifractal analysis. part i: Positive matrices. Israel J. Math., 138:353–376, 2003.
[2] D. J. Feng and K. S. Lau. The pressure function for products of non-negative matrices. Math. Res. Lett., 9:363–378, 2002.
[3] R. W. Kenyon and Y. Peres. Hausdorff dimension of affine-invariant sets. Israel J. Math., 94:157–178, 1996.
[4] T. J. Chen. Multi-fractal analysis for sofic shift. preprint.
[5] M. Boyle and Petersen. Hidden markov processes in the context of symbolic dynamics. preprint.
[6] P. Walters. An introduction to ergodic theory. Springer-Verlag Berlin Heidelberg New York, 1982. 1