4 citations · 5 across the 8 of their papers we have counts for
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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…
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 exhib…
On the dynamics of rotating rank-one strange attractors families
Alexandre A. P. Rodrigues, Bruno F. Gonçalves
In this article, we study a two-parameter family of rotating rank-one maps defined on , with , whose dynamics is charact…
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…
High frequency forcing of an attracting heteroclinic cycle
Isabel S. Labouriau, Alexandre A. P. Rodrigues
This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to i…
Differential equations with pulses: existence and stability of periodic solutions
Alexandre A. P. Rodrigues
We consider generic differential equations in with a finite number of hyperbolic equilibria, which are subject to --periodic instantaneous perturbative pulses ($ω>0…