This is a follow up to one of my previous questions on manifolds and state space. As I read through the answer, another question popped up in me.
1)Can there be a dynamic system with state space bounded ? Such as the states evolve only in a subset of R(n) if initial conditions lie in the subset.
2)Typically when I look at state equations there is invariably a mention that the states span R(n) space. Assuming a nonlinear dynamic system for which someone could give a single analytical state equation will it typically apply for all of R(n)? What if there are state constraints to the system, should a seperate state equation be defined at boundaries?