Limit set

In the theory of dynamical systems is called limit sets the points of the state space, which are approaching orbits (for positive or negative time ) infinitely often.

Definition

Be a dynamic system with or. Be a point of the state space.

The - limit set of

The - limit set of

Alternatively, limit sets can also be characterized as follows:

The limit sets are closed and invariant under. If is compact, the limit sets are not empty.

Types

• Fixed point
• Periodic Orbit
• Limit cycle
• Strange attractor