A Polynomial Class of Markus-Yamabe Counterexamples and Examples in ?3

We give a polynomial family of counterexamples to the Markus-Yamabe conjecture which contains and generalizes that of Cima-Gasull-Mañosas. Furthermore, we construct a new class of polynomial vector fields in ?3 having the origin as a global attractor which satisfy the Markus-Yamabe hypotheses. © 2011 Taylor & Francis.