Abstract
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 ℝ3 having the origin as a global attractor which satisfy the Markus–Yamabe hypotheses.
Acknowledgements
The authors were supported in part by FONDECYT Grant #1080172, by CONICYT Grant PBCT ADI 17, and by MATH–AMSUD DySET. The second author was also supported by FONDECYT Postdoctoral Grant #3100082.