possible dynamics on $\mathbb{R}^2$ A linear map is non-hyperbolic if $|\lambda_i|=1$ for a least one eigenvalue $\lambda_i$.
Catalogue the possible dynamics of a non-hyperbolic linear map on $\mathbb{R}^2$
For something like this would you go through all the cases;
i.e $|\lambda_1|=|\lambda_2|=1$ e.t.c?
Any hints on what all the cases are and mean would be great, thanks.

I would suggest the following. What happens if $|\lambda_1|=1$ and


*

*$|\lambda_2|<1$ ?

*$|\lambda_2|=1$ ?

*$|\lambda_2|>1$ ?


Do you think we need to consider the cases where we swap $1$ and $2$ in the indices above?
