A counterexamle to the strong real Jacobian conjecture

1994/09/01 by Sergey Pinchuk · 1 voice · 14 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · doi:10.1007/bf02571929

crossref issued 1994/09/01 · crossref published 1994/09/01 · crossref published-print 1994/09/01 · openalex publication_date 1994/09/01 · crossref created 2007/03/22 · crossref deposited 2019/05/20 · openalex created_date 2025/10/10 · crossref indexed 2026/07/03 · openalex updated_date 2026/07/28

Cited by

• Some geometrical aspects of control points for toric patches
• On the Rational Real Jacobian Conjecture
• An Optimization Approach to Jacobian Conjecture
• Integrating the Jacobian equation
• Picturing Pinchuk's Plane Polynomial Pair
• Differential and graphical approaches to multistability theory for chemical reaction networks
• A minimax principle to the injectivity of the Jacobian conjecture
• On quartic forms associated with cubic transformations of the real plane
• The intrinsic topology of linear maps
• A note on invertible quadratic transformations of the real plane
• Counterexamples to the Jacobian conjecture in dimensions greater than two
• A rough classification of potentially invertible cubic transformations of the real plane
• Conformal geometry, Euler numbers, and global invertibility in higher dimensions
• The Jacobian conjecture and injectivity conditions

Discussions

• Arguments against: - the past week - If you strengthen the conjecture to locally invertible maps, even over R, it's false (doi.org/10.1007/BF02...), [bsky, 3 points, 3 comments]