English

Normal Hyperbolicity in Secondary Hopf Bifurcations

Dynamical Systems 2025-07-16 v1 Classical Analysis and ODEs

Abstract

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.

Keywords

Cite

@article{arxiv.2507.10721,
  title  = {Normal Hyperbolicity in Secondary Hopf Bifurcations},
  author = {Pedro C. C. R. Pereira and Douglas D. Novaes},
  journal= {arXiv preprint arXiv:2507.10721},
  year   = {2025}
}

Comments

7 pages

R2 v1 2026-07-01T04:01:04.920Z