Volume 26, Issue 1
Contact Finite Determinacy of Relative Map Germs

Commun. Math. Res., 26 (2010), pp. 1-6.

Published online: 2021-05

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• Abstract

The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence (or $\mathcal{K}_{S,T}$ equivalence) and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, $f$ is finite determined relative to $\mathcal{K}_{S,T}$ if and only if there exists a positive integer $k$, such that $\mathcal{M}^k (n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.

• Keywords

$\mathcal{K}_{S,T}$ equivalent, the tangent space of an orbit, relative deformation, finite determined relative to $\mathcal{K}_{S,T}$

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@Article{CMR-26-1, author = {Chen , Liang and Sun , Weizhi and Pei , Donghe}, title = {Contact Finite Determinacy of Relative Map Germs}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {1}, pages = {1--6}, abstract = {

The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence (or $\mathcal{K}_{S,T}$ equivalence) and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, $f$ is finite determined relative to $\mathcal{K}_{S,T}$ if and only if there exists a positive integer $k$, such that $\mathcal{M}^k (n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19172.html} }
TY - JOUR T1 - Contact Finite Determinacy of Relative Map Germs AU - Chen , Liang AU - Sun , Weizhi AU - Pei , Donghe JO - Communications in Mathematical Research VL - 1 SP - 1 EP - 6 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19172.html KW - $\mathcal{K}_{S,T}$ equivalent, the tangent space of an orbit, relative deformation, finite determined relative to $\mathcal{K}_{S,T}$ AB -

The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence (or $\mathcal{K}_{S,T}$ equivalence) and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, $f$ is finite determined relative to $\mathcal{K}_{S,T}$ if and only if there exists a positive integer $k$, such that $\mathcal{M}^k (n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.

LiangChen, WeizhiSun & DonghePei. (2021). Contact Finite Determinacy of Relative Map Germs. Communications in Mathematical Research . 26 (1). 1-6. doi:
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