A limit cycle is an isolated periodic orbit of a dynamical system. An attracting limit cycle is approached by nearby trajectories, while a repelling limit cycle is approached in reverse time.
Qin and Sun (2026) proved that the maximum number 
of limit cycles of a real planar polynomial vector field of degree
at most 
satisfies 
as 
, where 
is big-Omega notation.
This is a lower bound, not an upper bound or an exact value. Qin and Sun (2026) report
using GPT-5.6 Sol for proof strategies and Lean formalization.
