2011/06/03 by Álvaro Castañeda, Castañeda, Álvaro, Victor Guíñez +2
Mathematics · Physics and Astronomy · #37C10 #37C70 #37C75 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #math.DS #msc:37C10 #msc:37C70 #msc:37C75
paper · pdf · doi:10.48550/arxiv.1106.0755
openalex publication_date 2011/06/03 · arxiv created 2012/02/02 · arxiv updated 2012/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the discrete and continuous versions of the Markus- Yamabe Conjecture for polynomial vector fields in Rn (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.