### Abstract

Let a(λ), b(λ) j{cyrillic, ukrainian} C[λ], and let f_{λ}(x) j{cyrillic, ukrainian} C[x] be a one-parameter family of polynomials indexed by all λ j{cyrillic, ukrainian} C. We study whether there exist infinitely many λ j{cyrillic, ukrainian} C such that both a(λ) and b(λ) are preperiodic for f_{λ}.

Original language | English |
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Pages (from-to) | 701-732 |

Number of pages | 32 |

Journal | Algebra and Number Theory |

Volume | 7 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Sep 9 |

### Keywords

- Heights
- Preperiodic points

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Ghioca, D., Hsia, L. C., & Tucker, T. J. (2013). Preperiodic points for families of polynomials.

*Algebra and Number Theory*,*7*(3), 701-732. https://doi.org/10.2140/ant.2013.7.701