On polynomial submersions of degree 4 and the real Jacobian conjecture in \(\mathbb{R}^2\)

DOI10.1016/j.jmaa.2016.05.048zbMath1347.14011arXiv1406.7683OpenAlexW2592227833WikidataQ122963708 ScholiaQ122963708MaRDI QIDQ302016

Francisco Braun, Bruna Oréfice-Okamoto

Publication date: 4 July 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.7683

zbMATH Keywords

Jacobian conjecturepolynomial mappingreal Jacobian conjecture

Mathematics Subject Classification ID

Jacobian problem (14R15)

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Injectivity of non-singular planar maps with one convex component, A new sufficient condition in order that the real Jacobian conjecture in \(\mathbb{R}^2\) holds, On necessary and sufficient conditions for the real Jacobian conjecture, New lower bounds for the maximal number of inseparable leaves of nonsingular polynomial foliations of the plane, A generalization of the Poincaré compactification and the real Jacobian conjecture, Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space, A sufficient condition in order that the real Jacobian conjecture in \(\mathbb{R}^2\) holds, Very degenerate polynomial submersions and counterexamples to the real Jacobian conjecture, Dynamics, points and places at infinity, and the inversion of polynomial self-maps of \(\mathbb{R}^2\), A new class of non-injective polynomial local diffeomorphisms on the plane, A sufficient condition for the real Jacobian conjecture in \(\mathbb{R}^2\), Foliations, solvability, and global injectivity

Cites Work

• Unnamed Item
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• Non-positive curvature and global invertibility of maps
• Invertible polynomial mappings via Newton non-degeneracy
• Global asymptotic stability for differentiable vector fields of \(\mathbb R^2\)
• Algebraic and topological classification of the homogeneous cubic vector fields in the plane
• A counterexample to the strong real Jacobian conjecture
• Note on estimation of the number of the critical values at infinity
• Polynomial automorphisms and the Jacobian conjecture
• The Jacobian matrix and global univalence of mappings
• The real Jacobian conjecture on \(\mathbb R^2\) is true when one of the components has degree 3
• The Real Jacobian Conjecture for polynomials of degree 3
• Injective Morphisms of Real Algebraic Varieties
• Global Injectivity ofC¹Maps of the Real Plane, Inseparable Leaves and the Palais–Smale Condition