3 citations · 8 across the 10 of their papers we have counts for
11 papers
On the family of trajectories of an analytic gradient flow converging to a critical point
Zbigniew Szafraniec
There are presented sufficient conditions for existence of an infinite family of trajectories of an analytic gradient flow which converge to a critical point.
On the stable set of an analytic gradient flow
Zbigniew Szafraniec
In this paper we study the stable set of the gradient flow associated with a critical point of an analytic function. In particular we present simple topological conditions which im…
On bifurcation of cusps
Zbigniew Szafraniec
Let f_t , where t is close to zero, be an analytic family of plane-to-plane mappings. There are presented effective methods of computing the number of cusps of f_t emanating from t…
Counting indices of critical points of rank two of polynomial selfmaps of R^4
Zbigniew Szafraniec
There is shown how to compute the sum of indices of critical points of rank two for polynomial selmaps of R^4
Mappings from R^3 to R^3 and signs of swallowtails
Justyna Bobowik, Zbigniew Szafraniec
Let M be an oriented 3-manifold. For a generic f \in C^ \infty(M,R^3), there is a discrete set of swallowtail critical points. In that case, at any swallowtail point p there exists…
On polynomial mappings from the plane to the plane
Iwona Krzyżanowska, Zbigniew Szafraniec
Let f be a generic polynomial mapping mapping from the plane to the plane. There are constructed quadratic forms whose signatures determine the number of positive and negative cusp…