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Dimensions of Level-1 Group-Based Phylogenetic Networks. [PDF]

Bull Math Biol
Gross E, Krone R, Martin S.
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A Generalization of the Poincaré Compactification and the Real Jacobian Conjecture

Journal of Dynamics and Differential Equations, 2022
The author develops a generalization to Poincaré compactification of polynomial vector fields on \(\mathbb{R}^2\). She then uses this compactification to provide new sufficient conditions for the validity of the real Jacobian conjecture for certain conditions on the relevant weight-homogeneous polynomials.
Claudia Valls, Valls Claudia
exaly   +3 more sources

A weight-homogenous condition to the real Jacobian conjecture in

Proceedings of the Edinburgh Mathematical Society, 2021
AbstractIt is known that a polynomial local diffeomorphism $(f,\, g): {\mathbb {R}}^{2} \to {\mathbb {R}}^{2}$ is a global diffeomorphism provided the higher homogeneous terms of $f f_x+g g_x$ and $f f_y+g g_y$ do not have real linear factors in common. Here, we give a weight-homogeneous framework of this result. Our approach uses qualitative theory of
Francisco Braun, Claudia Valls
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Very degenerate polynomial submersions and counterexamples to the real Jacobian conjecture

Journal of Pure and Applied Algebra, 2023
The authors give a counterexample to the real Jacobian conjecture, which is different from the Pinchuk maps. The degree of the counterexample is 9. Moreover, the authors calculate the asymptotic variety and asymptotic flower of the counterexample.
Braun, Francisco, Fernandes, Filipe
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Completely Mixed Games And Real Jacobian Conjecture

1997
In this paper, we consider Cubic Linear Mapping F : Rn → Rn, where Fi = Xi + (AX) i 3 , X ∈ Rn, i = 1,2,…n A is an n x n matrix and study the injectivity of F when A is a P0 matrix or when A is a Z matrix. In the sequel, we also derive many interesting results related to cubic linear mappings .In our proofs, we make use of concepts from game theory.
T. Parthasarathy, S. Ravindran, Sabatini, Marco   +2 more
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A counterexample to a folk real Jacobian conjecture

Israel Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Braun, Francisco, Fernandes, Filipe
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The Real Jacobian Conjecture for polynomials of degree 3

Annales Polonici Mathematici, 2001
The paper solves the famous real Jacobian conjecture in the following particular case: If \((f,g):\mathbb R^2\to\mathbb R^2\) is a polynomial mapping such that \(\deg f\leq 3\), \(\deg g\leq 3\) and the Jacobian \(\text{Jac}(f,g)\) of \((f,g)\) is strictly positive in \(\mathbb R^2\), i.e. \(\text{Jac}(f,g)(x)>0\) for every \(x\in \mathbb R^2\), then \(
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A new sufficient condition in order that the Real Jacobian Conjecture in ℝ² holds

Proceedings of the American Mathematical Society
Let ( f , g ) :
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On Necessary and Sufficient Conditions for the Real Jacobian Conjecture

Qualitative Theory of Dynamical Systems, 2023
Yulin Zhao, Zhao Yulin
exaly