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. I...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.展开更多
In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
Given a reflexive Banach space X .In the ring of C ∞ function germs ε(X) ,any real singular germ f in ε(X) whose second Frechet derivative at origin f″(0)=T is a Fredholm operator is isomorp...Given a reflexive Banach space X .In the ring of C ∞ function germs ε(X) ,any real singular germ f in ε(X) whose second Frechet derivative at origin f″(0)=T is a Fredholm operator is isomorphic to a germ of the form 12<Tz,z>+g(v) .If we replace g by a g 1 which is isomorphic to g ,we clearly obtain a germ in ε(X) which is isomorphic to the original one. However,is true converse of this proposition?In this paper,we will show that the converse is also true.展开更多
基金Supported by the National Natural Science Foundation of China(11671070,11501051)NSF of Heilongjiang Province of China(QC2016008)the Project of Science and Technology of Jilin Provincial Education Department(JJKH2090547KJ)
文摘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.
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
文摘Given a reflexive Banach space X .In the ring of C ∞ function germs ε(X) ,any real singular germ f in ε(X) whose second Frechet derivative at origin f″(0)=T is a Fredholm operator is isomorphic to a germ of the form 12<Tz,z>+g(v) .If we replace g by a g 1 which is isomorphic to g ,we clearly obtain a germ in ε(X) which is isomorphic to the original one. However,is true converse of this proposition?In this paper,we will show that the converse is also true.
