Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910431202770944 |
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| author | Bournez, Olivier Gozzi, Riccardo |
| author_facet | Bournez, Olivier Gozzi, Riccardo |
| contents | We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value problems and we prove that for this class of problems the unique solution can always be obtained analytically via transfinite recursion. We present several examples including a nontrivial one whose solution yields, at an integer time, a real encoding of the halting set for Turing machines; therefore showcasing that the behavior of solvable systems is related to ordinal Turing computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations Bournez, Olivier Gozzi, Riccardo Computational Complexity Logic in Computer Science Dynamical Systems We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value problems and we prove that for this class of problems the unique solution can always be obtained analytically via transfinite recursion. We present several examples including a nontrivial one whose solution yields, at an integer time, a real encoding of the halting set for Turing machines; therefore showcasing that the behavior of solvable systems is related to ordinal Turing computations. |
| title | Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations |
| topic | Computational Complexity Logic in Computer Science Dynamical Systems |
| url | https://arxiv.org/abs/2405.00165 |