Dont think so sir

Dear Satish Gummadi

Generally, linear and nonlinear systems have infinite state space representations. Since, we can define different states. 

If you mean uniqueness in sense that solution doesn't cross each other, then answer is no. Examples are almost periodic points: consider logistic map x_(n+1)=a*x_n*(1-x_n), with two initial condition 1 and 0 you receive 0. But if you means that given previous state, can we determine next state of system, then answer is yes. In simple word, general function f(x_n), is a function but it's one-to-one function.