On the Z2 index of global attractor for odd dynamical systems and application

In this paper, by applying Z₂ index, we are concerned with the geometry of global attractor for odd dynamical systems, we extend the results in [1] for p-Laplacian to general odd dynamical systems, to be precise, we firstly prove that the global attractor for odd dynamical systems is symmetric if it exists, and then the lower bound of Z₂ index of the symmetric global attractor is estimated. As application, we consider the Z₂ index of global attractors for reaction-diffusion equation with polynomial nonlinearity of odd power terms.