## Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current

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- by Yûsuke Okuyama
- Conform. Geom. Dyn.
**18**(2014), 217-228 - DOI: https://doi.org/10.1090/S1088-4173-2014-00271-9
- Published electronically: November 12, 2014
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## Abstract:

We establish an approximation of the activity current $T_c$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is a superattracting periodic point. This partly generalizes a Dujardin–Favre theorem for rational functions having preperiodic points, and refines a Bassanelli–Berteloot theorem on a similar approximation of the bifurcation current $T_f$ of the holomorphic family $f$. The proof is based on a dynamical counterpart of this approximation.## References

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## Bibliographic Information

**Yûsuke Okuyama**- Affiliation: Division of Mathematics, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585 Japan
- Email: okuyama@kit.ac.jp
- Received by editor(s): February 24, 2014
- Received by editor(s) in revised form: July 11, 2014, and August 12, 2014
- Published electronically: November 12, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**18**(2014), 217-228 - MSC (2010): Primary 37F45
- DOI: https://doi.org/10.1090/S1088-4173-2014-00271-9
- MathSciNet review: 3276585