Collision-Free Dynamical Systems

Collision-freeness is an important structural property of particle dynamics. A nonlinear ODE system ẋ(t) = f(x(t)) is called collision-free if the solution to the initial value problem with x(0)=x° has distinct components for all times t whenever the initial state x° has distinct components. Both the general case of a C1–function f and the special case of a polynomial (or even linear) function f will be addressed.