7 papers · 1 filter
Periodic forcing of a heteroclinic network
Isabel S. Labouriau, Alexandre A. P. Rodrigues
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential e…
Asymptotic stability of robust heteroclinic networks
Olga Podvigina, Sofia B. S. D. Castro, Isabel S. Labouriau
We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heter…
Chaos in periodically forced reversible vector fields
Isabel S. Labouriau, Elisa Sovrano
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~ reversible vector fields and…
Recognition of symmetries in reversible maps
Patrícia H. Baptistelli, Isabel S. Labouriau, Miriam Manoel
We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries an…
Periodic Functions, Lattices and Their Projections
Isabel S. Labouriau, Eliana M. Pinho
Functions whose symmetries form a crystallographic group in particular have a lattice of periods, and the set of their level curves forms a periodic pattern. We show how after proj…
Bifurcations from an attracting heteroclinic cycle under periodic forcing
Isabel S. Labouriau, Alexandre A. P. Rodrigues
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attrac…