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An elementary way to find a counterexample to the Jacobian Conjecture
Abstract
We show how a counterexample to the Jacobian Conjecture can be found by elementary mathematics. The example we find is, apart from linear coordinate changes the example found by Levent Alpöge.
Related
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- Some arithmetical aspects of the two dimensional Jacobian Conjecture
- Global injectivity and real Jacobian conjecture in ℝn
- Poincaré compactifications of pullbacks of parallel vector fields under counterexamples to the real Jacobian conjecture
- The generalized Dixmier conjecture and the two-dimensional Jacobian conjecture
BibTeX
@misc{essen2026elementary,
title = {{An elementary way to find a counterexample to the Jacobian Conjecture}},
author = {Arno van den Essen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17795},
eprint = {2609.17795},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17795},
}
RIS
TY - UNPB
TI - An elementary way to find a counterexample to the Jacobian Conjecture
AU - Arno van den Essen
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17795
UR - https://arxiv.org/abs/2609.17795
AB - We show how a counterexample to the Jacobian Conjecture can be found by elementary mathematics. The example we find is, apart from linear coordinate changes the example found by Levent Alpöge.
ER -