@article{a9689503-1820-3725-a886-dd400a74d56d,
    issn = {00029939, 10886826},
    url = {http://www.jstor.org/stable/23807735},
    abstract = {In this paper, we first show that homogeneous Keller maps are injective on lines through the origin. We subsequently formulate a generalization which states that under some conditions, a polynomial endomorphism with r homogeneous parts of positive degree does not have r times the same image point on a line through the origin, in case its Jacobian determinant does not vanish anywhere on that line. As a consequence, a Keller map of degree r does not take the same values on r > 1 collinear points, provided r is a unit in the base field. Next, we show that for invertible maps x + H of degree d such that ker J H has n − r independent vectors over the base field, in particular for invertible power linear maps x + (Ax)*d with rk A = r, the degree of the inverse of x + H is at most dr.},
    author = {DAN YAN and MICHIEL DE BONDT},
    journal = {Proceedings of the American Mathematical Society},
    number = {2},
    pages = {391--400},
    publisher = {American Mathematical Society},
    title = {SOME REMARKS ON THE JACOBIAN CONJECTURE AND POLYNOMIAL ENDOMORPHISMS},
    urldate = {2023-11-22},
    volume = {142},
    year = {2014},
    date-added = {2023-11-22 8:38:12 +0100}
}

@article{a9689503-1820-3725-a886-dd400a74d56d, issn = {00029939, 10886826}, url = {http://www.jstor.org/stable/23807735}, abstract = {In this paper, we first show that homogeneous Keller maps are injective on lines through the origin. We subsequently formulate a generalization which states that under some conditions, a polynomial endomorphism with r homogeneous parts of positive degree does not have r times the same image point on a line through the origin, in case its Jacobian determinant does not vanish anywhere on that line. As a consequence, a Keller map of degree r does not take the same values on r > 1 collinear points, provided r is a unit in the base field. Next, we show that for invertible maps x + H of degree d such that ker J H has n − r independent vectors over the base field, in particular for invertible power linear maps x + (Ax)*d with rk A = r, the degree of the inverse of x + H is at most dr.}, author = {DAN YAN and MICHIEL DE BONDT}, journal = {Proceedings of the American Mathematical Society}, number = {2}, pages = {391--400}, publisher = {American Mathematical Society}, title = {SOME REMARKS ON THE JACOBIAN CONJECTURE AND POLYNOMIAL ENDOMORPHISMS}, urldate = {2023-11-22}, volume = {142}, year = {2014}, date-added = {2023-11-22 8:38:12 +0100} }