When studying dynamical systems with continuous variables, moving from $1$ dimension to $2$ to $3$ introduces qualitatively different phenomena (under certain conditions):
- going from $n=1$ to $n=2$, introduces the possibility of cyclical systems.
- going from $n=2$ to $n=3$, introduces the possibility of chaotic behavior.
Are there any qualitatively different phenomena introduced by going from $n=3$ to $n=4$, i.e. phenomena that cannot occur in $n=3$?