Abstract
In this paper a parametrized Newton-Kantorovich approach is applied to continuation of periodic orbits in arbitrary polynomial vector fields. This allows us to rigorously validate numerically computed branches of periodic solutions. We derive the estimates in full generality and present sample continuation proofs obtained using an implementation in Matlab. The presented approach is applicable to any polynomial vector field of any order and dimension. A variety of examples is presented to illustrate the efficacy of the method.
| Original language | English |
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| Pages (from-to) | 59-97 |
| Number of pages | 39 |
| Journal | Journal of Computational Dynamics |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2021 |
Funding
2020 Mathematics Subject Classification. Primary: 37C27, 34A12; Secondary: 65G40. Key words and phrases. Validated numerics, periodic orbits, continuation, solution branch, polynomial ODEs. The authors are partially supported by NWO-VICI grant 639033109.
Keywords
- continuation
- periodic orbits
- polynomial ODEs
- solution branch
- Validated numerics