姓名 |
陳玎如(Ting-Ju Chen)
查詢紙本館藏 |
畢業系所 |
數學系 |
論文名稱 |
在Sofic Shift上的多重碎型分析 (Multi-fractal Analysis for Sofic Shift)
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相關論文 | |
檔案 |
[Endnote RIS 格式]
[Bibtex 格式]
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摘要(中) |
在本篇論文中,我們研究矩陣值勢能在sofic 系統上的譜維度。考慮跟有限座標有關的正矩陣值勢能,透過建構quasi-Bernoulli測度得到譜維度,而且利用有限逼近的方法,我們可以把結論推廣到跟無限座標有關的矩陣值勢能的情況上。最後,我們給一個可以確切算出譜維度的例子。
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摘要(英) |
We study the dimension spectrum of sofic system with the potential which is matrix-valued. For positive and finite-coordinate dependent matrix potential, we set up the dimension spectrum by constructing the quasi-Bernoulli measure and the cut-off method is applied to deal with the infinite-coordinate dependent case. Finally, we give an example which we can compute the spectrum concretely.
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關鍵字(中) |
★ Sofic 系統 ★ Gibbs-like 測度 ★ 有限逼近法 ★ 譜維度 |
關鍵字(英) |
★ sofic system ★ Gibbs-like measure ★ cut-off method ★ Dimension spectrum |
論文目次 |
中文摘要…………………………………………………i
英文摘要…………………………………………………ii
Contents ………………………………………………iii
1 Introduction …………………………………………1
2 Proof of Theorem A …………………………………5
3 Proof of Theorem B …………………………………14
4 Example ………………………………………………18
References …………………………………………………22
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參考文獻 |
[1] D. J. Feng and K. S. Lau. The pressure function for products of nonnegative
matrices. Math. Res. Lett., 9:363–378, 2002.
[2] D. Lind and B. Marcus. An introduction to symbolic dynamics and coding.
Cambridge University Press, Cambridge, 1995.
[3] B. Kitchens. Symbolic dynamics. One-sided, two-sided and countable state
Markov shifts. Springer-Verlag, New York, 1998.
[4] P.Walters. An Introduction to ergodic theory. Springer-Verlag, New York,
1982.
[5] E. Olivier. Uniqueness of the measure with full dimension on sofic affineinvariant
subsets of the 2-torus. Ergodic Theory Dynam. Systems, 2009.
[6] R. W. Kenyon and Y. Peres. Hausdorff dimension of affine-invariant sets.
Israel J. Math., 94:157–178, 1996.
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指導教授 |
許正雄(Cheng-Hsiung Hsu)
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審核日期 |
2011-6-27 |
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