Differential system

Existence and uniqueness of continuous flows

Let 𝐹 :ℝ𝑛 →ℝ𝑛 be differentiable. Then for each 𝑥0 ∈ℝ𝑛 there exists 𝑇 >0 such that ˙𝑥 =𝐹(𝑥) has a unique solution 𝑞(𝑡,𝑥0) for 𝑡 ∈( −𝑇,𝑇) with 𝑞(0,𝑥0) =𝑥0.¹ #m/thm/dynamics/flow

Consequences

• Trajectories cannot intersect or merge in finite time.

#state/tidy | #lang/en | #SemBr