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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.03247 |
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| _version_ | 1866914535879737344 |
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| author | Bravo, J. L. Trinidad-Forte, R. |
| author_facet | Bravo, J. L. Trinidad-Forte, R. |
| contents | We characterize global centers (all solutions are periodic) of the piecewise linear equation $x'=a(t)|x| + b(t)$ when the coefficients $a,b$ are trigonometric polynomials, under some generic hypotheses.
We prove that the global centers are those determined by the composition condition on $a,b$. That is, the equation has a global center if and only if there exist polynomials $P, Q$ and a trigonometric polynomial $h$ such that $a(t)=P(h(t))h'(t)$, $b(t)=Q(h(t))h'(t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Centers in Piecewise linear Differential Equations in the Cylinder Bravo, J. L. Trinidad-Forte, R. Classical Analysis and ODEs We characterize global centers (all solutions are periodic) of the piecewise linear equation $x'=a(t)|x| + b(t)$ when the coefficients $a,b$ are trigonometric polynomials, under some generic hypotheses. We prove that the global centers are those determined by the composition condition on $a,b$. That is, the equation has a global center if and only if there exist polynomials $P, Q$ and a trigonometric polynomial $h$ such that $a(t)=P(h(t))h'(t)$, $b(t)=Q(h(t))h'(t)$. |
| title | Global Centers in Piecewise linear Differential Equations in the Cylinder |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.03247 |