In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe ...In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.展开更多
CONSIDER a C<sup>l</sup> （l≥3） area-preserving diffeomorphism f: U→R<sup>2</sup>, defined in a neighbourhoodU of origin O in a plane and assume that f（O）=O and Df（O） has a pair of pure ...CONSIDER a C<sup>l</sup> （l≥3） area-preserving diffeomorphism f: U→R<sup>2</sup>, defined in a neighbourhoodU of origin O in a plane and assume that f（O）=O and Df（O） has a pair of pure imaginaryeigenvalues e<sup>±iω<sub>0</sub></sup> ω<sub>0</sub>≠2πm/n, i. e. origin O is an elliptic fixed point of f. In generic casesone can write f=B+C, where the ristriction of B to each circle p<sup>2</sup>+q<sup>2</sup>=2τis a展开更多
In this paper, we compute lower dimensional volumes Vol_4^((1,1)) and Vol_6^((2,2)) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler–Kalau–Walze typ...In this paper, we compute lower dimensional volumes Vol_4^((1,1)) and Vol_6^((2,2)) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler–Kalau–Walze type theorems. We also give theoritic explaination of the gravitational action for 4, 6 dimensional manifolds with boundary by these noncommutative residues.展开更多
In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive （n ＋ 2）-dimensional Lebesgue measure in the neighborhood of an elliptic ...In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive （n ＋ 2）-dimensional Lebesgue measure in the neighborhood of an elliptic equilibrium provided that its lineaxized system at the equilibrium satisfies some small divisor conditions. Both of the invariant sets are foliated by two-dimensional invaxiant tori carrying quasi-oeriodic solutions.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10801027Fok Ying Tong Education Foundation under Grant No.121003
文摘In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.
文摘CONSIDER a C<sup>l</sup> （l≥3） area-preserving diffeomorphism f: U→R<sup>2</sup>, defined in a neighbourhoodU of origin O in a plane and assume that f（O）=O and Df（O） has a pair of pure imaginaryeigenvalues e<sup>±iω<sub>0</sub></sup> ω<sub>0</sub>≠2πm/n, i. e. origin O is an elliptic fixed point of f. In generic casesone can write f=B+C, where the ristriction of B to each circle p<sup>2</sup>+q<sup>2</sup>=2τis a
基金Science Foundation for(Grant No.BS423)Inner Mongolia Natural Science Foundation for(Grant No.2018LHO1004)
文摘In this paper, we compute lower dimensional volumes Vol_4^((1,1)) and Vol_6^((2,2)) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler–Kalau–Walze type theorems. We also give theoritic explaination of the gravitational action for 4, 6 dimensional manifolds with boundary by these noncommutative residues.
基金Supported by NNSF of China (Grant 10531050)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070284004)
文摘In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive （n ＋ 2）-dimensional Lebesgue measure in the neighborhood of an elliptic equilibrium provided that its lineaxized system at the equilibrium satisfies some small divisor conditions. Both of the invariant sets are foliated by two-dimensional invaxiant tori carrying quasi-oeriodic solutions.
