A new class of non-injective polynomial local diffeomorphisms on the plane. (English) Zbl 1474.14081
Summary: In this short note we provide the example with the lowest degree known so far of a non-injective local polynomial diffeomorphism \(F=(p,q):\mathbb{R}^2\to\mathbb{R}^2\). In our example \(p\) has degree 10 and \(q\) has degree 15, rather than 10 and 25, respectively, known up to now as the smallest degrees for the coordinates of \(F\). Our construction was based on S. Pinchuk’s celebrated counterexample to the real Jacobian conjecture [7].
MSC:
| 14R15 | Jacobian problem |
References:
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