## Mating, paper folding, and an endomorphism of $\mathbb {P}\mathbb {C}^2$

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- by Volodymyr Nekrashevych
- Conform. Geom. Dyn.
**20**(2016), 303-358 - DOI: https://doi.org/10.1090/ecgd/302
- Published electronically: November 22, 2016
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## Abstract:

We are studying topological properties of the Julia set of the map $F(z, p)=\left (\left (\frac {2z}{p+1}-1\right )^2, \left (\frac {p-1}{p+1}\right )^2\right )$ of the complex projective plane $\mathbb {P}\mathbb {C}^2$ to itself. We show a relation between this rational function and an uncountable family of “paper folding” plane filling curves.## References

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## Bibliographic Information

- Received by editor(s): March 2, 2016
- Received by editor(s) in revised form: September 15, 2016
- Published electronically: November 22, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**20**(2016), 303-358 - MSC (2010): Primary 37F15, 37F20
- DOI: https://doi.org/10.1090/ecgd/302
- MathSciNet review: 3574443

Dedicated: In memory of Vitaly Sushchansky