### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- Heights
- Preperiodic points

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Algebra and Number Theory*,

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

**Preperiodic points for families of polynomials.** / Ghioca, Dragos; Hsia, Liang Chung; Tucker, Thomas J.

Research output: Contribution to journal › Article

*Algebra and Number Theory*, vol. 7, no. 3, pp. 701-732. https://doi.org/10.2140/ant.2013.7.701

}

TY - JOUR

T1 - Preperiodic points for families of polynomials

AU - Ghioca, Dragos

AU - Hsia, Liang Chung

AU - Tucker, Thomas J.

PY - 2013/9/9

Y1 - 2013/9/9

N2 - Let a(λ), b(λ) j{cyrillic, ukrainian} C[λ], and let fλ(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 fλ.

AB - Let a(λ), b(λ) j{cyrillic, ukrainian} C[λ], and let fλ(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 fλ.

KW - Heights

KW - Preperiodic points

UR - http://www.scopus.com/inward/record.url?scp=84883346552&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883346552&partnerID=8YFLogxK

U2 - 10.2140/ant.2013.7.701

DO - 10.2140/ant.2013.7.701

M3 - Article

AN - SCOPUS:84883346552

VL - 7

SP - 701

EP - 732

JO - Algebra and Number Theory

JF - Algebra and Number Theory

SN - 1937-0652

IS - 3

ER -