Normal Hyperbolicity in Secondary Hopf Bifurcations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912482685091840 |
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| author | Pereira, Pedro C. C. R. Novaes, Douglas D. |
| author_facet | Pereira, Pedro C. C. R. Novaes, Douglas D. |
| contents | We combine results available in the literature to prove that the torus emerging in a secondary Hopf bifurcation is normally hyperbolic. This result is then applied to establish sufficient conditions for the bifurcation of normally hyperbolic invariant tori in the extended phase space of systems with small time-periodic perturbations via an application of the averaging method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal Hyperbolicity in Secondary Hopf Bifurcations Pereira, Pedro C. C. R. Novaes, Douglas D. Dynamical Systems Classical Analysis and ODEs 34C45, 34C29 We combine results available in the literature to prove that the torus emerging in a secondary Hopf bifurcation is normally hyperbolic. This result is then applied to establish sufficient conditions for the bifurcation of normally hyperbolic invariant tori in the extended phase space of systems with small time-periodic perturbations via an application of the averaging method. |
| title | Normal Hyperbolicity in Secondary Hopf Bifurcations |
| topic | Dynamical Systems Classical Analysis and ODEs 34C45, 34C29 |
| url | https://arxiv.org/abs/2507.10721 |