网页Dynamical Systems: A Brief Introduction. 1. Objects of Study. Phase Space. M : A geometric object (e.g. sphere, tori, open set in. Rn). System. : A mapping. → M . Orbits: x → T (x) → T (T (x)) → . Ex1: = R1, T : R1 7→R1 defined by. (x) = 1 − 2x 2. = 0.1, x1 = 0.98, x2 = −0.9208, . Ex2: M = S1, T (θ) = θ + π. θ = 1, θ1 = 1 + π, θ2 = 1, . Ex3: