3 papers
math.DS2026
The Bosch and Simó conjecture on the Shilnikov-Hopf bifurcation
Alexandre A. P. Rodrigues
We provide a rigorous mathematical proof of the Bosch-Simó conjecture ( M. Bosch, C. Simó (1993), Physica D, 217--229) regarding the abundance of strange attractors in the unfoldin…
math.DS2025
Three-dimensional horseshoes near an unfolding of a Hopf-Hopf singularity
Santiago Ibáñez, Alexandre A. P. Rodrigues
Motivated by a certain type of unfolding of a Hopf-Hopf singularity, we consider a one-parameter family of --vector fields in whose flows exh…
math.DS2024
Transitions of bifurcation diagrams of a forced heteroclinic cycle
Isabel S. Labouriau, Alexandre A. P Rodrigues
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of map…