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1.
Shyūichi Izumiya 《manuscripta mathematica》1986,56(2):125-134
In the previous paper [3], we have developed a smooth classification theory of zero point sets of parametrized smooth map germs. In this paper we study a topological classification theory. It is closely related to Y. H. Wan's theory in [5]. 相似文献
2.
光滑映射芽的有限决定性是奇点理论中一个重要专题 .对函数芽的有限决定性问题 ,主要是在右等价群及其一些子群作用下来讨论的 .本文在 [1]和 [4 ]的基础上讨论函数芽在右等价群的正规子群 R*n (S;n)作用下的有限决定性 ,并组出函数芽有限 R*r (S;n) -决定的一个充分必要条件 . 相似文献
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4.
光滑映射芽的开折的分级稳定性 总被引:3,自引:0,他引:3
光滑映射芽各种稳定性的讨论,一直是奇点理论的一个重要部分. Thom R.[1]在创立突变论时,提出了映射芽的,r-开折的稳定性理论.Wassermann G.[2]将之发展为开折的(r,s)稳定理论.本文将他们的结论发展为(r1,r2,…,rd)稳定性,在任意的分级情况下,得到强稳定性、弱稳定性及无穷小稳定性的等价性,并得到了一些基本结果. 相似文献
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6.
V. A. Timorin 《Functional Analysis and Its Applications》2004,38(1):45-51
Consider a smooth map of a neighborhood of the origin in a real vector space into a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though the origin to the same circles as a Hopf map coming from a representation of a Clifford algebra. We also describe a connection between our result and the Hurwitz–Radon theorem about sums of squares. 相似文献
7.
We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion and that the multiplicity function is constant. We provide some applications of this regularity result, especially in the calculus of variations for the area functional. © 2020 Wiley Periodicals LLC 相似文献
8.
Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented. 相似文献
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10.
Given a finite map germ f : (X, 0) → (Y, 0) between complex analytic reduced space curves, we look at invariants which control the topological triviality and the Whitney equisingularity in families of this type of map germs. In the case that (Y, 0) is smooth, the main invariant is the Milnor number of a function on a curve. We deduce some applications to the equisingularity of families of finitely determined map germs ${f : (\mathbb{C}^2, 0) \to (\mathbb{C}^2, 0)}$ and ${f : (\mathbb{C}^2, 0) \to (\mathbb{C}^3, 0)}$ . 相似文献
11.
We introduce the concept of topological finite-determinacy for
germs of analytic functions within a fixed ideal
I, which provides a notion of topological finite-determinacy
of functions with non-isolated singularities. We prove the following statement
which generalizes classical results of Thom and Varchenko: let
A be the complement in the ideal I of the space
of germs whose topological type remains unchanged under a
deformation within the ideal that only modifies sufficiently
large order terms of the Taylor expansion. Then A has infinite
codimension in I in a suitable sense. We also prove the
existence of generic topological types of families of germs of
I parametrized by an irreducible analytic set. 相似文献
12.
We consider interactions of smooth and discontinuous germs as generalized integrations over non‐rectifiable paths with applications in theory of boundary value problems of complex analysis. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
13.
Bifurcations of ordinary differential equations of Clairaut type 总被引:1,自引:0,他引:1
Masatomo Takahashi 《Journal of Differential Equations》2003,190(2):579-599
We classify a one-parameter family of Clairaut-type equations. In order to pursue the classification, we use legendrian singularity theory and the notion of one-parameter complete legendrian unfoldings which induces a special class of divergent diagrams of map germs which are called one-parameter integral diagrams. Our normal forms are represented by one-parameter integral diagrams. 相似文献
14.
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs
of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation
on roundings and prove that any rounding, whose differential at 0 has rank at least 2, is equivalent to a fractional quadratic
rounding. A fractional quadratic map is just the ratio of a quadratic map and a quadratic polynomial. We also show that any
rounding gives rise to a quadratic map between spheres. The known results on quadratic maps between spheres have some interesting
implications concerning roundings.
Partially supported by CRDF RM1-2086. 相似文献
15.
Nguyen Le Hoang Anh 《Positivity》2017,21(4):1527-1543
In the paper, the higher-order contingent derivative of a parametrized set-valued inclusion is first established. For its applications, we obtain sensitivity analysis of solution map in the decision variable space for a parametrized constrained set-valued optimization problem in terms of higher-order contingent derivatives. 相似文献
16.
Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric
solutions of such systems are classified by using versal deformation and the classification of stable map germs of type Σ1 in singularity theory. 相似文献
17.
余维数不大于3的(D3,O(2))-等变分歧问题的分类 总被引:1,自引:0,他引:1
本文利用奇点理论中光滑映射芽的接触等价,研究状态变量和分歧参数均具有对称性的分歧问题,对状态变量具有D3对称性,分岐参数具有O(2)对称性且余维数小于等于3的等变分歧问题进行分类,并给出了相应的识别条件. 相似文献
18.
Jiro Adachi 《Mathematische Zeitschrift》2013,273(3-4):711-733
The conditions to determine germs of Engel structures relative to arbitrary subsets are studied. We show that germs of Engel structures at a point relative to an arbitrary subset are determined by the algebraic restrictions of the Engel structures themselves to the subset, and the projected algebraic restrictions of the derived even-contact structures to the subset. When the subset is a smooth submanifold, algebraic restriction is equivalent to geometric restriction. Even when the subset is a smooth submanifold, we need a new stricter notion, projected algebraic restriction. 相似文献
19.
In this paper we give some conclusions on Newton non-degenerate analytic map germs on Kn (K = ? or ?), using information from their Newton polyhedra. As a consequence, we obtain the exact value of the Lojasiewicz exponent at the origin of Newton non-degenerate analytic map germs. In particular, we establish a connection between Newton non-degenerate ideals and their integral closures, thus leading to a simple proof of a result of Saia. Similar results are also considered to polynomial maps which are Newton non-degenerate at infinity. 相似文献