Real-time dynamical system
A real-time dynamical system or a real dynamical system or flow is a triple where:
- is an open nonempty interval in the reals, containing zero
- is a differential manifold
- is a map where
if both sides are defined
To each let . Then is open in . We can them define a map:
given as .
- is termed the evolution function
- is called the phase space or state space
- is called the evolution parameter
- is called the initial state of the system
- The map is termed the flow at and its graph the trajectory through . Its image is termed the orbit of
- A subspace of is said to be -invariant if for all for which .