A note on the orbit equivalence of global attractors for S1-equivariant parabolic equations

Carlos Rocha

Published 2024-03-22Version 1

Here we clarify the proof of Theorem 3 of \cite{roc12} about the characterization of global attractors $\cA_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of nonlinearities called of simple type. We modify the proof to make it simpler and amenable to generalization. In addition, we extend this result to the general case of nonlinearities $f=f(u,u_x)$ obtaining a complete orbit equivalence for the global attractors.