The aim of this paper is to share with the mathematical community a list of 33 problems that I
have found along the years in my research. I believe that it is worth to think about them and …

Motivated by some notorious open problems, such as the Jacobian conjecture and the tame
generators problem, the subject of polynomial automorphisms has become a rapidly …

Oligopoly theory is one of the most intensively studied areas of mathematical economics. On
the basis of the pioneering works of Cournot (1838), many researchers have developed and …

A polynomial counterexample to the Markus-Yamabe Conjecture Page 1 A polynomial
counterexample to the Markus-Yamabe Conjecture Anna Cima∗, Arno van den Essen‡ …

Nonautonomous Dynamics Page 1 Springer Monographs in Mathematics David N. Cheban
Nonautonomous Dynamics Nonlinear Oscillations and Global Attractors Page 2 Springer …

The main result of this paper asserts that it suffices to prove the Jacobian Conjecture for all
polynomial maps of the form $ x+ H $, where $ H $ is homogeneous (of degree 3) and $ JH …

(a) Let X: R 2→ R 2 be a differentiable map (not necessarily C1) and let Spec (X) be the set
of (complex) eigenvalues of the derivative DXp when p varies in R 2. If, for some ε> 0, Spec …

Second-order counterexample to the discrete-time Kalman conjecture Page 1 Second-order
counterexample to the discrete-time Kalman conjecture Joaquin Carrasco1, William P. Heath1 …

In this article, the author gives counterexamples to the Linear Dependence Problem for
Homogeneous Nilpotent Jacobians for dimension 5 and up. This problem has been …

Let k be a field of characteristic zero and F: k3→ k3 a polynomial map of the form F= x+ H,
where H is homogeneous of degree d⩾ 2. We show that the Jacobian Conjecture is true for …