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71.
Consider two circle homeomorphisms fi∈C2+α(S?{bi}), α>0, i=1,2 with a single break point bi i.e. a discontinuity in the derivative Dfi, and identical irrational rotation number ρ. Suppose the jump ratios and do not coincide. Then the map ψ conjugating f1 and f2 is a singular function i.e. it is continuous on S1 and Dψ(x)=0 a.e. with respect to Lebesgue measure. 相似文献
72.
设$f$是紧tvs锥度量空间上同胚映射. 本文证明了$f$是tvs锥可扩的当且仅当$f$有生成元. 进一步, 如果$f$是tvs锥可扩的,则具有收敛半轨的点集是可数集. 本文的这些结果改进了拓扑动力系统的一些可扩同胚定理, 将有助于研究tvs锥度量空间上同胚映射的动力性质. 相似文献
73.
Zbigniew Leśniak 《Journal of Difference Equations and Applications》2016,22(7):853-864
We prove that the set of all regular points of a flow of Brouwer homeomorphisms is invariant under topological equivalence of flows. We also show that a similar result holds for the first prolongational limit set. 相似文献
74.
Mike Hurley 《Proceedings of the American Mathematical Society》1996,124(4):1305-1309
We show that if is a compact manifold, then there is a residual subset of the set of homeomorphisms on with the property that if , then the periodic points of are dense in its chain recurrent set. This result was first announced in [4], but a flaw in that argument was noted in [1], where a different proof was given. It was recently noted in [5] that this new argument only serves to show that the density of periodic points in the chain recurrent set is generic in the closure of the set of diffeomorphisms. We show how to patch the original argument from [4] to prove the result.
75.
The complementarity problem with a nonlinear continuous mappingf from the nonnegative orthantR
+
n
ofR
n intoR
n can be written as the system of equationsF(x, y) = 0 and(x, y) R
+
2n
, whereF denotes the mapping from the nonnegative orthantR
+
2n
ofR
2n intoR
+
n
× Rn defined byF(x, y) = (x
1y1,,xnyn, f1(x) – y1,, fn(x) – yn) for every(x, y) R
+
2n
. Under the assumption thatf is a uniformP-function, this paper establishes that the mappingF is a homeomorphism ofR
+
2n
ontoR
+
n
× Rn. This result provides a theoretical basis for a new continuation method of tracing the solution curve of the one parameter family of systems of equationsF(x, y) = tF(x
0, y0) and(x, y) R
+
2n
from an arbitrary initial point(x
0, y0) R
+
2n
witht = 1 until the parametert attains 0. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving linear complementarity problems with positive semi-definite matrices. 相似文献
76.
退化拟共形映射的整体同胚与二维奇异积分方程 总被引:1,自引:0,他引:1
设D是一个边界Г∈Ca1(0<a≤1)的有界单连通域,复函数q(z)∈Ca1,|q(z)|≤1,等式只能在Г上成立,且在Г上等式q(z(t))z′(t)/z′(t)+1|z∈Г=0最多在有限个点上成立.本文给出了复伸张q(z)满足上述条件时的退化拟共形映射的整体同胚解及以q(z)为系数的一类二维奇异积分方程的解. 相似文献
77.
Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms 下载免费PDF全文
Yun Ping JIANG 《数学学报(英文版)》2020,36(3):245-272
Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide. 相似文献
78.
79.
本文证明, 紧度量空间上的同胚, 若在链回复集上可扩且具有伪轨跟踪性, 则是链拓扑稳定的. 相似文献
80.