Qualitatively new phenomena with $4$ dimensional dynamical systems?

183 Views Asked by At

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 $n=3$?