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

We present two new classes of polynomial maps satisfying the real Jacobian conjecture in R2. The first class is formed by the polynomials maps of the form (q(x) - p(y),q(y) + p(x)): R2 → R2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by poly...

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Detalhes bibliográficos
Autores: Itikawa, Jackson|||0000-0002-8268-0016, Llibre, Jaume|||0000-0002-9511-5999
Formato: artículo
Fecha de publicación:2019
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221324
Acesso em linha:https://ddd.uab.cat/record/221324
https://dx.doi.org/urn:doi:10.1590/0001-3765201920170627
Access Level:acceso abierto
Palavra-chave:Injective polynomial maps
Global center
Real Jacobian conjecture
Planar Hamiltonian systems
Descrição
Resumo:We present two new classes of polynomial maps satisfying the real Jacobian conjecture in R2. The first class is formed by the polynomials maps of the form (q(x) - p(y),q(y) + p(x)): R2 → R2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f,g): R2 → R2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.