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  1. (, Ergodic Theory and Dynamical Systems)
    Katok’s special representation theorem states that any free ergodic measure-preserving R^d-flow can be realized as a special flow over a Z^d-action. It provides a multidimensional generalization of the ‘flow under a function’ construction. We prove the analog of Katok’s theorem in the framework of Borel dynamics and show that, likewise, all free Borel R^d-flows emerge from Z^d-actions through the special flow construction using bi-Lipschitz cocycles. 
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