文摘
Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615006683&_mathId=si133.gif&_user=111111111&_pii=S0022039615006683&_rdoc=1&_issn=00220396&md5=4e3a1e0292eda329dc9f1450945a8a65" title="Click to view the MathML source">F=(f,g):R2→R2class="mathContainer hidden">class="mathCode"> be a polynomial map such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615006683&_mathId=si3.gif&_user=111111111&_pii=S0022039615006683&_rdoc=1&_issn=00220396&md5=97b2f025160216155a9de14166ece9f6" title="Click to view the MathML source">detDF(x,y)class="mathContainer hidden">class="mathCode"> is different from zero for all class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615006683&_mathId=si140.gif&_user=111111111&_pii=S0022039615006683&_rdoc=1&_issn=00220396&md5=35343c1c2fb50d946224ee5b9622a10a" title="Click to view the MathML source">(x,y)∈R2class="mathContainer hidden">class="mathCode"> and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615006683&_mathId=si11.gif&_user=111111111&_pii=S0022039615006683&_rdoc=1&_issn=00220396&md5=1f9ab7748603426d0b8bb64450d8212d" title="Click to view the MathML source">F(0,0)=(0,0)class="mathContainer hidden">class="mathCode">. We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of the polynomials class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615006683&_mathId=si12.gif&_user=111111111&_pii=S0022039615006683&_rdoc=1&_issn=00220396&md5=3e077d1d82140159318700360e411160" title="Click to view the MathML source">ffx+ggxclass="mathContainer hidden">class="mathCode"> and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039615006683&_mathId=si13.gif&_user=111111111&_pii=S0022039615006683&_rdoc=1&_issn=00220396&md5=579ac9160c152714a77c42731f295dd0" title="Click to view the MathML source">ffy+ggyclass="mathContainer hidden">class="mathCode"> do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.