Looking for a surjection or R^2

I am looking for a smooth surjection of R^2 onto itself, not bijective, with jacobian everywhere not zero. My best example so far is an holomorphic function (with the obvious isomorphism between C and R^2) like the antiderivative of exp(z^2) (which is surjective by Picard theorem), but I would like something simpler, more explicit, and where the proof of surjectivity uses only elementary calculations...
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