Hadamard-Lévy theorems for maps taking values in a finite dimensional space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908589326598144 |
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| author | Chitour, Yacine Ji, Zhengping Trélat, Emmanuel |
| author_facet | Chitour, Yacine Ji, Zhengping Trélat, Emmanuel |
| contents | We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional Euclidean space, when its second-order differential has uniform upper and lower bounds, it has a global path-lifting property in the presence of singularities. This is then applied to the nonlinear motion planning problem, establishing in some cases the well-posedness of the continuation method despite critical values of the endpoint maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hadamard-Lévy theorems for maps taking values in a finite dimensional space Chitour, Yacine Ji, Zhengping Trélat, Emmanuel Classical Analysis and ODEs Optimization and Control We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional Euclidean space, when its second-order differential has uniform upper and lower bounds, it has a global path-lifting property in the presence of singularities. This is then applied to the nonlinear motion planning problem, establishing in some cases the well-posedness of the continuation method despite critical values of the endpoint maps. |
| title | Hadamard-Lévy theorems for maps taking values in a finite dimensional space |
| topic | Classical Analysis and ODEs Optimization and Control |
| url | https://arxiv.org/abs/2510.11206 |