MathDBBosch–Simó strange-attractor conjecture
Bosch–Simó strange-attractor conjecture
For a dissipative dynamical system undergoing a Shilnikov–Hopf bifurcation, the Bosch–Simó conjecture predicts that, in the parameter unfolding, chaotic and periodic regimes are interspersed and that there is a parameter set of positive Lebesgue measure for which the associated return dynamics possesses a large strange attractor in the sense of Broer–Simó–Tatjer.
Sources & referencesView supporting material
Primary source
Additional references
Progress summary
An unrefereed manuscript claims to prove the conjecture, but no independent confirmation has appeared.
The Bosch–Simó conjecture, formulated by M. Bosch and C. Simó in 1993, concerns the abundance of strange attractors near a Shilnikov–Hopf bifurcation. It predicts chaotic behavior interspersed with periodic regimes in the associated return dynamics.
August 2026 claimed proof
Alexandre A. P. Rodrigues’s manuscript claims a rigorous proof: positive-measure parameter sets have large strange attractors carrying unique ergodic Sinai–Ruelle–Bowen measures, while other parameters yield superstable periodic orbits. The claim is unrefereed, with no independent verification, error report, or withdrawal found.
Current status (as of August 2026): A manuscript claims to settle the Bosch–Simó conjecture, but the result remains unverified; no counterexample or substantive objection has been reported in the retrieved sources.
Sources
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.