Rigorous existence of a single attractor

Prove the existence of a single attractor for the dissipative Labyrinthic map in parameter regimes where numerical trajectories show a preference for convergence to one attractor.

Background

Section 5 presents numerical parameter-space analyses of the dissipative Labyrinthic map (DLM). For small values of the parameter a, the authors observe that trajectories tend to converge to periodic attractors or to the quasi-periodic shearless attractor, with a numerical tendency toward a single attractor. They explicitly state that a rigorous existence proof for this attractor has not been obtained.

References

It is important to note that while there is a preference for a single attractor in the phase space, rigorous proof of its existence remains elusive.

— Shearless and periodic attractors in the dissipative Labyrinthic map  (2610.26534 - B. et al., 19 Oct 2026) in Section 5, Shearless attractors scenarios