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 - <p style="text-align: justify;">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 $\mathcal{M}^k
(n)Ԑ(S; n)^p ⊂ T\mathcal{K}_{S,T}(f)$.</p>