Nielsen方程Mei对称性导致的一种新型守恒量

研究完整系统Nielsen方程Mei对称性导致的一种新型守恒量.在群的无限小变换下,由Nielsen方程Mei对称性的定义和判据,得到完整系统Nielsen方程Mei对称性导致的新型结构方程和新型守恒量.举例说明结果的应用. 关键词： Nielsen方程 Mei对称性 新型结构方程 新型守恒量     

Nielsen Methods and Groups Acting on Hyperbolic Spaces

We show that for any n & in there exists a constant C(n) such that any n-generated group G which acts by isometries on a -hyperbolic space (with >0) is either free or has a nontrivial element with translation length at most C(n).     

Computation of Nielsen numbers for maps of closed surfaces

Let be a closed surface, and let be a map. We would like to determine Nielsen fixed point theory provides a lower bound for , called the Nielsen number, which is easy to define geometrically and is difficult to compute.

We improve upon an algebraic method of calculating developed by Fadell and Husseini, so that the method becomes algorithmic for orientable closed surfaces up to the distinguishing of Reidemeister orbits. Our improvement makes tractable calculations of Nielsen numbers for many maps on surfaces of negative Euler characteristic. We apply the improved method to self-maps on the connected sum of two tori including classes of examples for which no other method is known. We also include the application of this algebraic method to maps on the Klein bottle . Nielsen numbers for maps on were first calculated (geometrically) by Halpern. We include a sketch of Halpern's never published proof that for all maps on .

     

Nielsen fixed point theory for partially ordered sets

In this paper, we introduce a Nielsen type number for any selfmap f of a partially ordered set of spaces. This Nielsen theory relates to various existing Nielsen type fixed point theories for different settings such as maps of pairs of spaces, maps of triads, fibre preserving maps, equivariant maps and iterates of maps, by exploring their underlying poset structures.     

A nontrivial example of application of the Nielsen fixed-point theory to differential systems: Problem of Jean Leray

In reply to a problem posed by Jean Leray in 1950, a nontrivial example of application of the Nielsen fixed-point theory to differential systems is given. So the existence of two entirely bounded solutions or three periodic (harmonic) solutions of a planar system of ODEs is proved by means of the Nielsen number. Subsequently, in view of T. Matsuoka's results in Invent. Math. (70 (1983), 319-340) and Japan J. Appl. Math. (1 (1984), no. 2, 417-434), infinitely many subharmonics can be generically deduced for a smooth system. Unlike in other papers on this topic, no parameters are involved and no simple alternative approach can be used for the same goal.

     

幂等自映照的Nielsen数

设X是一个有限且连通的多面体,f是x上的一个好幂等自映照,则f的Nielsen数不超过1.     

On the location of fixed points on pairs of spaces

Let f: (X, A)→(X, A) be an admissible selfmap of a pair of metrizable ANR's. A Nielsen number of the complement Ñ(f; X, A) and a Nielsen number of the boundary ñ(f; X, A) are defined. Ñ(f; X, A) is a lower bound for the number of fixed points on C1(X - A) for all maps in the homotopy class of f. It is usually possible to homotope f to a map which is fixed point free on Bd A, but maps in the homotopy class of f which have a minimal fixed point set on X must have at least ñ(f; X, A) fixed points on Bd A. It is shown that for many pairs of compact polyhedra these lower bounds are the best possible ones, as there exists a map homotopic to f with a minimal fixed point set on X which has exactly Ñ(f; X - A) fixed points on C1(X−A) and ñ(f; X, A) fixed points on Bd A. These results, which make the location of fixed points on pairs of spaces more precise, sharpen previous ones which show that the relative Nielsen number N(f; X, A) is the minimum number of fixed points on all of X for selfmaps of (X, A), as well as results which use Lefschetz fixed point theory to find sufficient conditions for the existence of one fixed point on C1(X−A).     

不动点大类与 Nielsen数

通过引进 π１ （ Ｘ,ｘ０ ） 的同态 ｆπ 的不动子群 Ｆｉｘｆπ,在 Ｈ ＝ Ｆｉｘｆπ ·ｋｅｒｆ π为π１ （ Ｘ,ｘ０ ） 的正规子群时定义了不动点大类,得到不动点大类数是有限的．在曲面 Ｘ的正则复迭空间 Ｘ Ｈ 为有限叶时只要姜子 群相对于 Ｈ 极大,ｆ 的 Ｎｉｅｌｓｅｎ 数就可以用一维同调群计算