## Abstract

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, |zmin| ≤ |z| ≤ |zmax|. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius r. We prove that if the moduli converge to r = |zmax| then the sequence of eigenstates is associated with a fixed phase space measure ρmax. The same holds for sequences with eigenvalue moduli converging to |zmin|, with a different limit measure ρmin. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius |zmin| <r <|zmax| there is no unique limit measure, and we identify some families of eigenstates with precise self-similar properties.

Translated title of the contribution | On the resonance eigenstates of an open quantum baker map |
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Original language | English |

Article number | 2591 |

Number of pages | 34 |

Journal | Nonlinearity |

Volume | 21 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2008 |