Topological Causality in Dynamical Systems.

@article{Harnack2017TopologicalCI,
  title={Topological Causality in Dynamical Systems.},
  author={Daniel Harnack and Erik Laminski and Maik Sch{\"u}nemann and Klaus R. Pawelzik},
  journal={Physical review letters},
  year={2017},
  volume={119 9},
  pages={
          098301
        }
}
Determination of causal relations among observables is of fundamental interest in many fields dealing with complex systems. Since nonlinear systems generically behave as wholes, classical notions of causality assuming separability of subsystems often turn out inadequate. Still lacking is a mathematically transparent measure of the magnitude of effective causal influences in cyclic systems. For deterministic systems we found that the expansions of mappings among time-delay state space… 

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