## Abstract

For a class of quadratic polynomial endomorphisms f : ℂ^{2} → ℂ^{2} close to the standard torus map (x, y) → (x_{2}, y_{2}), we show that the Julia set J(f) is homeomorphic to the torus. We identify J(f) as the closure ℛ of the set of repelling periodic points and as the Shilov boundary of the set K(f) of points with bounded forward orbit. Moreover, it turns out that (J(f),f) is a mixing repeller and supports a measure of maximal entropy for f which is uniquely determined as the harmonic measure for K(f).

Original language | English (US) |
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Pages (from-to) | 139-159 |

Number of pages | 21 |

Journal | Fundamenta Mathematicae |

Volume | 157 |

Issue number | 2-3 |

State | Published - 1998 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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