Persistence of the main results under higher-order remainders

Establish that the existence of abundant large strange attractors, SRB measures, and superstable periodic orbits proved for the leading-order Shilnikov–Hopf return map remains valid when the higher-order remainder terms are retained.

Background

The paper derives and analyzes a leading-order first return map for a Shilnikov–Hopf bifurcation after disregarding higher-order terms. Its principal conclusions concern the abundance of large strange attractors carrying SRB measures and the occurrence of superstable periodic sinks. The authors explicitly conjecture that these conclusions persist for the more complete return map including the omitted remainders, indicating that robustness with respect to those terms remains unresolved.

References

As in , we have disregarded higher-order terms to focus on the leading-order dynamics of $\mathcal{R}_b$. However, following the same reasoning of Prop. 2.1, we conjecture that our main results remain valid if we consider these remainders.

— The Bosch and Simó conjecture on the Shilnikov-Hopf bifurcation  (2608.13021 - Rodrigues, 13 Aug 2026) in Section “Discussion and concluding remarks,” subsection “Concluding remarks”