New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
Abstract: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.
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Academia Brasileira de Ciências
2019
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oai:scielo:S0001-376520190003002022019-06-27New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 ITIKAWA,JACKSONLLIBRE,JAUME injective polynomial maps global center real Jacobian conjecture planar Hamiltonian systems Abstract: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.info:eu-repo/semantics/openAccessAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências v.91 n.2 20192019-01-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652019000300202en10.1590/0001-3765201920170627 |
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ITIKAWA,JACKSON LLIBRE,JAUME |
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ITIKAWA,JACKSON LLIBRE,JAUME New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 |
| author_facet |
ITIKAWA,JACKSON LLIBRE,JAUME |
| author_sort |
ITIKAWA,JACKSON |
| title |
New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 |
| title_short |
New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 |
| title_full |
New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 |
| title_fullStr |
New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 |
| title_full_unstemmed |
New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 |
| title_sort |
new classes of polynomial maps satisfying the real jacobian conjecture in ℝ 2 |
| description |
Abstract: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions. |
| publisher |
Academia Brasileira de Ciências |
| publishDate |
2019 |
| url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652019000300202 |
| work_keys_str_mv |
AT itikawajackson newclassesofpolynomialmapssatisfyingtherealjacobianconjectureinr2 AT llibrejaume newclassesofpolynomialmapssatisfyingtherealjacobianconjectureinr2 |
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