On the real Jacobian conjecture and the center-type singularities
Augmented Lagrangian methods for constrained optimization using differentiable exa...
| Full text | |
| Author(s): |
Braun, Francisco
;
Fernandes, Filipe
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 227, n. 8, p. 10-pg., 2023-02-17. |
| Abstract | |
Until recently, the only known examples of non-injective polynomial local diffeomor-phisms of the plane were the Pinchuk maps discovered in 1994. These maps have the form (p, q), where p is a fixed polynomial of degree 10, and q satisfies certain relation. The lowest possible degree of q in a Pinchuk map is 25. In 2021, with the same p of a Pinchuk map, another example was given with q of degree 15. Aiming to find different examples, with the first components having lower degrees, we look for polynomials of degree less than or equal to 9 sharing some properties with the polynomial p of a Pinchuk map. We find precisely one polynomial of degree 7 and some ones of degree 9. By using one of the polynomials of degree 9 in the first com-ponent we construct a non-injective polynomial local diffeomorphism of the plane, with degree 15.(c) 2023 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 20/14498-4 - Global injectivity of maps and related topics |
| Grantee: | Francisco Braun |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Projects - Thematic Grants |