arXiv subjects
Publications and source records attributed to Víctor Guíñez.
We present, in dimension $n \geq 3$, a survey of examples to: the Jacobian conjecture, the weak Markus--Yamabe conjecture. Furthermore, we show and construct new examples of vector fields where the origin is almost globally asymptotically stable by using the novel concept of density functions introduced by Rantzer.
We study the discrete and continuous versions of the Markus- Yamabe Conjecture for polynomial vector fields in R^n (especially when n = 3) of the form X = λI+H where λis a real number, I the identity map, and H a map with nilpotent Jacobian matrix JH. We consider the case where the rows of JH are linearly dependent over R and that where they are linearly independent over R. In the former, we find non-linearly triangularizable vector fields X for which the origin is a global attractor for both the continuous and the discrete dynamical systems generated by X. In the independent continuous case, we present a family of vector fields which have orbits escaping to infinity. In the independent discrete case, we present a large family of vector fields which have a periodic point of period 3.