New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ2

• Main Authors: JACKSON ITIKAWA, JAUME LLIBRE
• Format: Article
• Language: English
• Published: Academia Brasileira de Ciências
• Series: Anais da Academia Brasileira de Ciências
• Subjects: injective polynomial maps; global center; real Jacobian conjecture; planar Hamiltonian systems
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652019000300202&lng=en&tlng=en
• ISSN: 0001-3765; 1678-2690

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.