First-return maps as a unified renormalization scheme for dynamical systems.

@article{Procaccia1987FirstreturnMA,
  title={First-return maps as a unified renormalization scheme for dynamical systems.},
  author={Procaccia and Thomae and Tresser},
  journal={Physical review. A, General physics},
  year={1987},
  volume={35 4},
  pages={
          1884-1900
        }
}
We propose to look at first-return maps into a specified region of phase space as a basis for a unified renormalization scheme for dynamical systems. The choice of the region for first return is dictated by the symbolic dynamics (e.g., kneading sequence) of the relevant trajectories. The renormalization group can be formulated on the symbolic level, but once translated to maps it yields the said renormalization scheme. We show how the well-studied examples of the onset of chaos via period… CONTINUE READING

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