Types of attractors

Question

In studying dynamical systems and chaos theory, one usually gets across a classification that says that attractors can be of four basic types:

-fixed point (equilibrium)

-cyclic (periodic)

-torus (quasiperiodic)

-strange (chaotic)

This is usually an informal statement, but can we give a proof that this classification is complete, that is there is no fifth type of attractor?

Note: If this seems too hard to answer in general, let's stay in phase space $\mathbb{R}^{n}$ to not overcomplicate.

Answer 1

Maybe not another types but anothe clasiifications :

• based on the simplicity of finding basin of attraction in the phase space
• based on the speed of attraction ( superattracting, attracting, weakly attracting)

Adam

Answer 2

Another one if I may quickly add is known as a strange nonchaotic attractor (SNA). See: "https://en.wikipedia.org/wiki/Strange_nonchaotic_attractor" and references therein for starters.