From wild Lorenz-like to wild Rovella-like dynamics

Abstract

We consider a two-dimensional noninvertible map that was introduced by Bamón, Kiwi and Rivera-Letelier as a model of a wild Lorenz-like attractor in a vector field of dimension at least five; such an attractor contains an expanding equilibrium and a hyperbolic set with robust homoclinic tangencies. Advanced numerical techniques enable us to study how the stable, unstable and critical sets of the map change within the conjectured region of wild chaos in the transition from Lorenz-like to Rovella-like dynamics, that is, when the equilibrium of the vector field becomes contracting. We find numerical evidence for the existence of wild Rovella-like attractors, wild Rovella-like saddles and regions of multistability, where a Rovella-like attractor coexists with two fixed-point attractors. We identify bifurcations generating these different types of dynamics and compute them in two-parameter bifurcation diagrams.

Keywords:

• noninvertible planar map
• Lorenz-like attractor
• Rovella-like attractor
• wild hyperbolic set
• stable and unstable sets
• critical set

MCS/CCS/AMS Classification/CR Category numbers:

• 37D45
• 37G20
• 37G25
• 37G35
• 65P30

Acknowledgements

We thank Jan Kiwi for drawing our attention to the map (1(1) ) and Juan Rivera-Letelier for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.