# Global uniqueness and determinism in classical mechanics [duplicate]

Something always bugged me about Newton's equations (or, equivalently, Euler-Lagrange/Hamilton's): Determinism, which is the philosophical framework of classical mechanics, requires that, by completely knowing the state of a system at a given instant, $$\textbf{x}(t_0)$$ and the law by which the system evolves, which, in dynamics, looks something like $$m\ddot{\textbf{x}}=f(\textbf{x},\dot{\textbf{x}},t)$$ You know the exact state of the system at any instant, forwards in time and, when defined, backwards. But global uniqueness theorems state that, for this to be true, the function $$f$$ needs some properties, namely that it doesn't "blow up" anywhere in the domain (iirc it's enough for $$f$$ to be uniformly continous). My question then can be posed as such: are there any systems in which the forces that naturally arise violate the global existence/uniqueness theorems? And if so, then what does this tell us about the system?