Structural stability of planar quasihomogeneous vector fields
The authors consider the space \(H_{pqm}\) of planar vector fields of the form \((P,Q)\), where \(p,q,m\) are positive integers, \[ P=\sum a_{ij}x^iy^j,\quad Q=\sum b_{ij}x^iy^j, \] and the sums are taken over \((i,j)\) such that \(pi+qj=p-1+m\) and \(pi+qj=q-1+m\), respectively. They characterize the set \(\Omega_{pqm}\) of structurally stable fields in \(H_{pqm}\) (with respect to the coefficient topology), determine the number of topological equivalence classes in \(\Omega_{pqm}\), and prove an analog of the Grobman--Hartman theorem at the origin for a class of vector fields starting with a term \(X\in\Omega_{pqm}\).
scientific article; zbMATH DE number 6391414
scientific article