Orbits Flashcards
(8 cards)
What is an orbit?
A collection of points related by the evolution function of the dynamical system
Do different orbits intersect in phase space?
No, an orbit is a subset of phase space as part of partitioned sets of orbits that cannot intersect.
What are some of the different types of orbits in dynamical systems?
period, chaotic, asymptotically periodic
What is a periodic orbit?
A special type of solution for a dynamical system that repeats itself in time.
What is an ocillator?
A stable periodic orbit.
What is a limit cycle?
A limit cycle is a closed trajectory in 2D phase space where at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity.
What is a chaotic orbit?
Non-periodic with a lyapunov exponent greater than 1
What is asymptotically periodic?
If the orbit converges to periodic as n approaches infinity, or any orbit attracted to a sink.
