Classification in Active Dimension 2 for Weighted Residual Dynamics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908889399689216 |
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| author | Tian, James |
| author_facet | Tian, James |
| contents | We study weighted residual dynamics associated with a rank-one projection in finite dimension. The iteration reduces, after finitely many steps, to a nonlinear recursion on a stabilized active subspace. We prove that this recursion can be classified when the active dimension is two: either a transverse reducing direction persists unchanged, or the coupled part collapses completely. As a consequence, we obtain a description of the limit in the active two-dimensional case and identify the threshold beyond which higher-dimensional behavior becomes more flexible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15291 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification in Active Dimension 2 for Weighted Residual Dynamics Tian, James Functional Analysis Primary: 47B65, secondary: 15B48, 47A64, 47J25 We study weighted residual dynamics associated with a rank-one projection in finite dimension. The iteration reduces, after finitely many steps, to a nonlinear recursion on a stabilized active subspace. We prove that this recursion can be classified when the active dimension is two: either a transverse reducing direction persists unchanged, or the coupled part collapses completely. As a consequence, we obtain a description of the limit in the active two-dimensional case and identify the threshold beyond which higher-dimensional behavior becomes more flexible. |
| title | Classification in Active Dimension 2 for Weighted Residual Dynamics |
| topic | Functional Analysis Primary: 47B65, secondary: 15B48, 47A64, 47J25 |
| url | https://arxiv.org/abs/2603.15291 |