2018/11/09 by Castañeda, Álvaro, Machado-Higuera, Maximiliano
#14R15 #37C10 #37C75 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.03891
In this article we study maps with nilpotent Jacobian in ℝn distinguishing the cases when the rows of JH are linearly dependent over ℝ and when they are linearly independent over ℝ. In the linearly dependent case, we show an application of such maps on dynamical systems, in particular, we construct a large family of almost Hurwitz vector fields for which the origin is an almost global attractor. In the linearly independent case, we show explicitly the inverse maps of the counterexamples to Generalized Dependence Problem and proving that this inverse maps also have nilpotent Jacobian with rows linearly independent over ℝ.