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<p>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.</p>

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Normal Hyperbolicity in Secondary Hopf Bifurcations

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Douglas D. Novaes,
  • Pedro C. C. R. Pereira

摘要

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.