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81.
82.
Zbigniew Le?niak 《Journal of Mathematical Analysis and Applications》2010,366(1):310-373
We present a method for finding continuous (and consequently homeomorphic) orientation preserving iterative roots of a Brouwer homeomorphism which is embeddable in a flow. To obtain the roots we use a countable family of maximal parallelizable regions of the flow which is a cover of the plane. The maximal parallelizable regions are unions of equivalence classes of an appropriate equivalence relation. We show that if an equivalence class is invariant under the nth iterate of a Brouwer homeomorphism g, then it is invariant under g. We use this fact to prove that each maximal parallelizable region of the flow must be invariant under all homeomorphic orientation preserving iterative roots of the given Brouwer homeomorphism. 相似文献
83.
A renormalization group transformation R
1 has a single stable point
in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number
(the golden mean). Let a homeomorphism T be the C
1-conjugate of
. We let
denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any
, the sequence
has a finite limiting distribution function
, which is continuous in
, and singular on the interval [0,1]. We also study the sequence
for k>1. 相似文献
84.
We study effective presentations and homeomorphisms of effective topological spaces. By constructing a functor from the category of computable models into the category of effective topological spaces, we show in particular that there exist homeomorphic effective topological spaces admitting no hyperarithmetical homeomorphism between them and there exist effective topological spaces whose autohomeomorphism group has the cardinality of the continuum but whose only hyperarithmetical autohomeomorphism is trivial. It is also shown that if the group of autohomeomorphisms of a hyperarithmetical topological space has cardinality less than 2
then this group is hyperarithmetical. We introduce the notion of strong computable homeomorphism and solve the problem of the number of effective presentations of T
0-spaces with effective bases of clopen sets with respect to strong homeomorphisms. 相似文献
85.
A. A. Saakyan 《Mathematical Notes》2003,74(1-2):255-265
In this paper, we prove that for any compact set
there exists a homeomorphism of the closed interval
such that for an arbitrary function f the Fourier series of the function F(x,y) = f((x),(y)) converges uniformly on
simultaneously over rectangles, over spheres, and over triangles. 相似文献
86.
87.
本文研究了超空间上的Wnitney映射,给出了它的一些性质和一个反例,从而解决了文献[1]中的一个问题. 相似文献
88.
A. B. Bogatyrev 《Mathematical Notes》2000,67(6):699-706
We consider a parameterization of the set of polynomialsT
n(E, x) whose deviation from zero is the least on a systemE consisting of several intervals on the real axis. We point out a new way for obtaining the equations which describe the boundary
of the maximum set of the least deviationE
+ ⊃E. We describe the geometry of the variety of all possible setsE
+; this manifold is embedded in the moduli space of hyperelliptic curves with real branch points.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 828–836, June, 2000. 相似文献
89.
90.
Zbigniew Leśniak 《Journal of Difference Equations and Applications》2019,25(9-10):1363-1371
ABSTRACTWe present properties of equivalence classes of the codivergency relation defined for a Brouwer homeomorphism for which there exists a family of invariant pairwise disjoint lines covering the plane. In particular, using the codivergency relation we describe the sets of regular and irregular points for such Brouwer homeomorphisms. Moreover, we show that under this assumption the interior of each equivalence class of this relation is invariant and simply connected. 相似文献