Limes amount

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In the theory of dynamic systems , limit sets (or limit value sets ) are those points in the state space that orbits approach infinitely often (for positive or negative time).

-Limes amount (limit cycle) of the van der Pol oscillator

definition

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

The limit set of is

.

The limit set of is

.

Alternatively, Limes sets can also be characterized as follows:

,
.

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

Types

literature