The Jacobian Conjecture: Approximate roots and intersection numbers
Jorge Alberto Guccione, Juan Jos\'e Guccione, Rodrigo Horruitiner and, Christian Valqui
TL;DR
This paper explores the Jacobian Conjecture by translating Xu's results into a new framework, providing formulas for intersection numbers with inequalities instead of equalities, advancing understanding of polynomial mappings.
Contribution
It introduces a translation of Xu's results into a different language, yielding approximate formulas for intersection numbers in the context of the Jacobian Conjecture.
Findings
Derived nearly the same formulas for intersection numbers
Replaced equalities with inequalities in the formulas
Enhanced understanding of polynomial mappings in the Jacobian Conjecture
Abstract
We translate the results of Yansong Xu into the language of~\cite{GGV1}, obtaining nearly the same formulas for the intersection number of Jacobian pairs, but with an inequality instead of an equality.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons · Quantum chaos and dynamical systems