文志雄
研究主要集中在非周期现象中的准晶理论的数学方法,离散动力系统,代换及有限自动机,分形几何等领域
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- 姓名:文志雄
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学术头衔:
博士生导师
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学科领域:
数理逻辑与数学基础
- 研究兴趣:研究主要集中在非周期现象中的准晶理论的数学方法,离散动力系统,代换及有限自动机,分形几何等领域
1981年毕业于武汉大学获硕士学位。1991年获法国南巴黎大学数学博士。1995年获法国指导科学研究资格。先后在武汉大学数学系、物理系任教。现为武汉大学基础与应用数学基地主任,教授,武汉工业与应用数学会理事长。国家973计划“非线性科学若干前沿课题”项目的骨干成员。先后在数学及物理的若干领域从事研究,在国内外有影响的刊物上已发表研究论文三十余篇。1995年以“自相似序列的研究及其应用”命名的课题获国家教委科技进步二等奖。近年来的研究主要集中在非周期现象中的准晶理论的数学方法,离散动力系统,代换及有限自动机,分形几何等领域,关于迹影射、可逆代换及分形的转移矩阵等研究成果处于国际前沿,都为国外著名刊物所采用,并多次被国际上的同行所引用。多次应邀到国外访问研究,在国际会议上报告工作。与法国南巴黎大学、法国国家科研中心(CNRS)马赛数学所有长期的合作关系。先后主持数项国家自然科学基金课题,国家攀登计划“非线性科学”项目(已结题)的正式成员。
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392
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成果数
9
文志雄 , Zhi-Ying WEN †, Yiping ZHANG †
,-0001,():
-1年11月30日
We consider the convolution transrms of measures on Rd defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function between the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behaviour of positive harmonic or parabolic functions on Rdal by multifractal analysis of measures.
Approximate identity,, Multifraetal,, Logarithmic density
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【期刊论文】Some remarks on invertible substitutions on three letter alphabet*
文志雄 , Wen Zhi-Xiong †, Zhang Yiping ‡
,-0001,():
-1年11月30日
We show by introducing the notion of "prime substitution" that the set of invertible substitutions over an alphabet of more than three letters is not finitely generated. Some examples are given.
invertible substitution,, prime substitution
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【期刊论文】A CLASS OF SELF-SIMILAR FRACTALS WITH OVERLAP STRUCTURE*
文志雄 , Rao Hui †, Wen Zhi-Ying ‡
,-0001,():
-1年11月30日
Consider the contracting similarities S1(x)=x/3, S2(x)=(x+λ)/3, S2(x)=(x+2)/3 where λε[0, 1]. Assuming Fλ is the invariant set with respect to S1, S2, and S3. In this paper, we study the Hausdorff measure, Hausdorff dimension and the structure of F. Letλ= b a 2 Q \ [0, 1], (a, b)=1. By using combinatorial techniques, we prove that |Fλ|>0 if a≡b 6≠0 (mod 3) and that in the other cases Fλ is a Cantor-like fractal with recursive construction.
Overlap,, Open set condition,, Hausdorff measure and dimension,, Fractal
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【期刊论文】HANKEL DETERMINANTS OF THE THUE-MORSE SEQUENCE
文志雄 , by J.-P. ALLOUCHE, J. PEYRI ERE, Z.-X. WEN (*), Z.-Y. WEN (**)
Ann. Inst. Fourier, Grenoble 48, 1 (1998), 1-27,-0001,():
-1年11月30日
Thue-Morse sequence, Period doubling sequence, Automatic sequences,
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【期刊论文】Some dimensional results for homogeneous Moran sets∗
文志雄 , FENG De-Jun, WEN Zhi-Ying, WU Jun
Science in China (Series A), 40(1997)475-482,-0001,():
-1年11月30日
Let M({nk}k≥1, {ck}k≥1) be the collection of homogeneous Moran sets deter-mined by {nk}k≥1 and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. In this paper, we determine the maximal and minimal values of Hausdorff dimensions for elements in M. We also prove that for any value s between the maximal and minimal values, there exists an element in M({nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to its. The same results hold for Packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.
Homogeneous Moran set,, Homogeneous Cantor set,, Partial homogeneous Cantor set,, Hausdorff dimension,, Packing dimension.,
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文志雄 , WEN Zhi-Xiong , , and WEN Zhi-Ying
Journal of Staistical Physies Vol. 75, Nos 341, 1994,-0001,():
-1年11月30日
Let F be the free group generated by the letters a and b. let φ be a homomorphism from P to SL2(¢). Lei χ=Trφ(a), y=Trφ(b), z=Trφ(ab) and let w ε F, then Trφ(w) will be a polynomial of variables x, y. z. The main aim of this note is to determine the leading term of Trφ(w). Let σ be an endomorphlsm of F, then σ witl indite a mapping φσ:(Z[x, y, z])3→(Z[x, y.=1)3 which is called the trace mapping associated with σ. We wig establish the recurrence relations of the reading terms and degrees of the iterations of φσ, Moreover, some typical examples are studied.
Trace mapping,, Substitution,, Leading tenn.,
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【期刊论文】Relations polynomiales entreles traces de produits de matrices
文志雄 , Zhi-Xiong WEN
C. R. Acad. Sci. Paris, t. 318, Serie I, p. 99-104, 1994,-0001,():
-1年11月30日
Nous donnons un procede permettant d'obtenir de nombreuses relations entre les traces Clans des algebres de matrices Cette 6rude fait suite a de nombreuses autres tant cn mathematlques ([1], [3], [7]a. [11], [13]) qu'cn physique (par cxemple, [2], [4], [5], [6]) ou ces relations permettent d'etudier le spectre de certains operateurs de Schredinger disrets, a potentiel defini par un automate fini, intervenant dans la modelisation des quasi-cristaux decouverts par Shechtman et al [12].
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【期刊论文】Some Properties of the Singular Words of the Fibonacci Word
文志雄 , WEN ZHI-XIONG, AND WEN ZHI-YING
Europ. J. Combinatorics (1994) 15, 587-598,-0001,():
-1年11月30日
The combinatorial properties of the Fibonacci infinite word are of great interest in some aspects of mathematics and physics, such as number theory, fractal geometry, formal language, computational complexity, quasicrystals etc. In this note, we introduce the singular words of the Fibonacci infinite word and discuss their properties. We establish two decompositions of the Fibonacci word in singular words and their consequences. By using these results, we discuss the local isomorphism of the Fibonacci word and the overlap properties of the factors. Moreover, we also give new proofs for the results on special words and the power of the factors.
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