A weight-homogenous condition to the real Jacobian conjecture in
| Autor: | Francisco Braun, Claudia Valls |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Proceedings of the Edinburgh Mathematical Society. 64:1028-1036 |
| ISSN: | 1464-3839 0013-0915 |
| DOI: | 10.1017/s0013091521000766 |
| Popis: | It 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 differential equations. In our reasoning, we obtain a result on polynomial Hamiltonian vector fields in the plane, generalization of a known fact. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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