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MATHER SETS FOR SUBLINEAR DUFFING EQUATIONS

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Chinese Annals of mathematics,Series B 1994年第4期15卷 421-434页

作者： QIAN DINGBIAN(department of mathematics, suzhou university, 215006, china.) 苏州大学数学系江苏苏州 215006

The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the applicat... 详细信息

关键词： Sublinear Duffing equation Finite twist Aubry-Mather theorem Mather sets.

P_(4k-1)-factorization of complete bipartite graphs

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Science china mathematics 2005年第4期48卷 539-547页

作者： DU Beiliang & WANG Jian department of mathematics, suzhou university, suzhou 215006, china Nantong Vocational College, Nantong 226007, china department of mathematics Suzhou University Suzhou China Nantong Vocational College Nantong China

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for the existence of Pv-factorization of Km,*** v is an odd number, Ushio in 1993 proposed a conjecture. However, up to now we only know that Ushio Conjecture is true for v = 3. In this paper we will show that Ushio Conjecture is true when v = 4k - 1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization of Km,n is (1) (2k - 1)m ≤ 2kn, (2) (2k -1)n≤2km, (3) m + n ≡ 0 (mod 4k - 1), (4) (4k -1)mn/[2(2k -1)(m + n)] is an integer.

关键词： complete bipartite graph, factorization, Ushio Conjecture.

The nonwandering set of some Hénon map

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Chinese Science Bulletin 1999年第7期44卷 590-594页

作者： CAO Yongluodepartment of mathematics , suzhou university, suzhou 215006, china department of mathematics Suzhou University Suzhou China

For the Hnon map Ta , b（x, y） = （1- ax2 + y, bx）, Benedicks and Carleson proved that for （ a, b） near （2, 0） and b > 0, there exists a set E with positive Lebesgue measure, whose corresponding map Ta,b possesses a strange attractor. Viana conjectured that if （a, b）∈ E, then the nonwandering set of the map Ta, b, Ω（Ta, b） = Aa,b U {qa, b},where A（a, b） is the strange attractor, qa, b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E1 E.

关键词： strange attractor nonwandering set. basin of attraction.

P_(4k-1)-factorization of bipartite multigraphs

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Science china mathematics 2006年第7期49卷 961-970页

作者： WANG Jian & DU Beiliang Nantong Vocational College, Nantong 226007, china department of mathematics, suzhou university, suzhou 215006, china Vocational College Nantong China department of mathematics Suzhou University Suzhou China

LetλKm,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A Pν-factorization ofλKm,n is a set of edge-disjoint Pν-factors ofλKm,n which partition the set of edges ofλKm,n. Whenνis an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a Pν-factorization ofλKm,n. When v is an odd number, we proposed a conjecture. However, up to now we only know that the conjecture is true forν= 3. In this paper we will show that the conjecture is true whenν= 4k-1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization ofλKm,n is (1) (2k-1)m≤2kn, (2) (2k-1)n≤2km, (3)m + n = 0 (mod 4k-1), (4)λ(4k-1)mn/[2(2k-1)(m + n)] is an integer.

关键词： bipartite multigraph, factor, factorization.

A characterization of the finite simple groups with set of indices of their maximal subgroups

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Science china mathematics 2004年第4期47卷 508-522页

作者： LI Xianhuadepartment of mathematics, suzhou university, suzhou 215006, china (email: xhli@***) department of mathematics Suzhou University Suzhou China

We study the problem concerning the influence of indices of maximal subgroups of a simple group on the structure of a group. We obtain a characterization property of all finite simple groups.

关键词： Finite simple group, maximal subgroup, index.

The spectrum for large sets of pure directed triple systems

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Science china mathematics 2006年第8期49卷 1103-1127页

作者： ZHOU Junling, CHANG Yanxun & Jl Lijun Institute of mathematics, Beijing Jiaotong university, Beijing 100044, china department of mathematics, suzhou university, suzhou 215006, china Institute of mathematics Beijing Jiaotong University Beijing China department of mathematics Suzhou University Suzhou China

An LPDTS(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTS(υ) for υ≡ 0,4 (mod 6), υ≥ 4. In this paper, we establish the existence of an LPDTS(υ) for υ≡ 1, 3 (mod 6), υ＞ 3. Thus the spectrum for LPDTS(υ) is completely determined to be the set {υ:υ≡0, 1 (mod 3),υ≥4}.

关键词： large set, oriented triple system, pure, directed candelabra system.

The proof of Ushio's conjecture concerning path factorization of complete bipartite graphs

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Science china mathematics 2006年第3期49卷 289-299页

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint Pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for existence of Pv-factorization of Km,n. When k is an odd number, Ushio in 1993 proposed a conjecture. Very recently, we have proved that Ushio's conjecture is true when v = 4k - 1. In this paper we shall show that Ushio Conjecture is true when v = 4k + 1, and then Ushio's conjecture is true. That is, we will prove that a necessary and sufficient condition for the existence of a P4k+1-factorization of Km,n is (i) 2km ≤ (2k + 1)n,(ii) 2kn ≤ (2k + 1)m, (iii) m + n ≡ 0 (mod 4k + 1), (iv) (4k + 1)mn/[4k(m + n)] is an integer.

关键词： complete bipartite graph, factorization, Ushio Conjecture.

The Geometric Structure of Strange Attractors in the Lozi Map

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Communications in Nonlinear Science and Numerical Simulation 1998年第2期3卷 67-71页

作者： Yongluo CAO and Zengrong LIU* (department of mathematics, suzhou university,suzhou 215006, china) *(department of mathematics, Shanghai university,Shanghai 200072, china) (E mail: ***) department of mathematics Suzhou University Suzhou 215006 China department of mathematics Shanghai University Shanghai 200072 China

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｓｔｔｗｏｄｅｃａｄｅｓ，ｔｈｅｓｔｒａｎｇｅａｔｒａｃｔｏｒｓｉｎｔｈｅｆｉｅｌｄｏｆｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅｄｒａｗｓｔｈｅａｔｅｎｔｉｏｎｏｆｍａｎｙｓｃｉｅｎｔｉ... 详细信息

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｓｔｔｗｏｄｅｃａｄｅｓ，ｔｈｅｓｔｒａｎｇｅａｔｒａｃｔｏｒｓｉｎｔｈｅｆｉｅｌｄｏｆｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅｄｒａｗｓｔｈｅａｔｅｎｔｉｏｎｏｆｍａｎｙｓｃｉｅｎｔｉｓｔｓ．Ｉｎｐａｒｔｉｃｕｌａｒ，...

关键词： strange attractor transversal homoclinic point weak transversal homoclinic point

A complexity analysis of the elementary cellular automaton of rule 122

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Chinese Science Bulletin 2001年第7期46卷 600-603页

作者： JIANG Zhisongmathematics department, suzhou university, suzhou 215006, china mathematics department Suzhou University Suzhou China

S. Wolfram initiated the use of formal languages and automata theory in study of cellular automata (CAs). By means of extensive experiments with computer, he classified all CAs into four classes and conjectured that the limit languages of the third class of CAs, which produce chaotic aperiodic behavior, are not regular. Using symbolic dynamics and formal languages, we prove that the limit language of the elementary CA of rule 122 is neither regular nor context-free.

关键词： cellular automaton formal language complexity limit language regular language context-free language.