### Abstract

Let φ(z) ∈ K (z) be a rational function of degree d ≥2 defined over a number field whose second iterate φ^{2}(z) is not a polynomial, and let α ∈ K. The second author previously proved that the forward orbit O_{φ}(α) contains only finitely many quasi-S-integral points. We give an explicit upper bound for the number of such points.

Original language | English |
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Pages (from-to) | 321-342 |

Number of pages | 22 |

Journal | Pacific Journal of Mathematics |

Volume | 249 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Feb 15 |

### Keywords

- Arithmetic dynamics
- Integral points

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Hsia, L. C., & Silverman, J. H. (2011). A quantitative estimate for quasiintegral points in orbits.

*Pacific Journal of Mathematics*,*249*(2), 321-342. https://doi.org/10.2140/pjm.2011.249.321