On backward stability of holomorphic dynamical systems

Volume 158 / 1998

G. Levin Fundamenta Mathematicae 158 (1998), 97-107 DOI: 10.4064/fm-158-2-97-107


For a polynomial with one critical point (maybe multiple), which does not have attracting or neutral periodic orbits, we prove that the backward dynamics is stable provided the Julia set is locally connected. The latter is proved to be equivalent to the non-existence of a wandering continuum in the Julia set or to the shrinking of Yoccoz puzzle-pieces to points.


  • G. Levin

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