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	Provedor de dados Anais da ABC (AABC) (4) Autor LLIBRE,JAUME (4) BRAUN,FRANCISCO (2) ARTÉS,JOAN CARLES (1) ITIKAWA,JACKSON (1) NOVAES,DOUGLAS D. (1) TEIXEIRA,MARCO A. (1) Mais... Palavra-chave Real Jacobian conjecture (3) Center (2) Global injectivity (2) Averaging theory (1) Bifurcation theory (1) Global center (1) Injective polynomial maps (1) Lienard differential equation (1) Periodic solution (1) Pinchuk map (1) Planar Hamiltonian systems (1) Poincaré compactification (1) Mais... Tipo do documento Info:eu-repo/semantics/article (4) Ano 2019 (1) 2018 (1) 2015 (2) País Brazil (4) Idioma Inglês (4)		Ordenar por:  Relevância Autor Título Ano Registros recuperados: 4 Primeira ... 1 ... Última A new qualitative proof of a result on the real jacobian conjecture Anais da ABC (AABC) BRAUN,FRANCISCO; LLIBRE,JAUME. Let F= (f, g) : R2 → R2be a polynomial map such that det DF(x) is different from zero for all x∈ R2. We assume that the degrees of fand gare equal. We denote by the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If do not have real linear factors in common, then F is injective. Tipo: Info:eu-repo/semantics/article Palavras-chave: Real Jacobian conjecture; Global injectivity; Center; Poincaré compactification. Ano: 2015 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000401519 New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 Anais da ABC (AABC) ITIKAWA,JACKSON; LLIBRE,JAUME. 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. Tipo: Info:eu-repo/semantics/article Palavras-chave: Injective polynomial maps; Global center; Real Jacobian conjecture; Planar Hamiltonian systems. Ano: 2019 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652019000300202 The phase portrait of the Hamiltonian system associated to a Pinchuk map Anais da ABC (AABC) ARTÉS,JOAN CARLES; BRAUN,FRANCISCO; LLIBRE,JAUME. Abstract In this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions, six of them of type strip and one annular. Tipo: Info:eu-repo/semantics/article Palavras-chave: Center; Global injectivity; Real Jacobian conjecture; Pinchuk map. Ano: 2018 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652018000602599 Periodic solutions of Lienard differential equations via averaging theory of order two Anais da ABC (AABC) LLIBRE,JAUME; NOVAES,DOUGLAS D.; TEIXEIRA,MARCO A.. Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ⁢ ( x ) ⁢ x ′ + n 2 ⁢ x + g ⁢ ( x ) = ε 2 ⁢ p 1 ⁢ ( t ) + ε 3 ⁢ p 2 ⁢ ( t ) , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 ⁢ π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained. Tipo: Info:eu-repo/semantics/article Palavras-chave: Periodic solution; Lienard differential equation; Averaging theory; Bifurcation theory. Ano: 2015 URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501905 Registros recuperados: 4 Primeira ... 1 ... Última

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