### Abstract

We consider suspension semi-flows of angle-multiplying maps on the circle for C^{r} ceiling functions with r3. Under a C^{r}generic condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L^{2} space such that the PerronFrobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the PerronFrobenius operator for the time-t-map is quasi-compact for a C^{r} open and dense set of ceiling functions.

Original language | English |
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Pages (from-to) | 291-317 |

Number of pages | 27 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 1 2008 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**Decay of correlations in suspension semi-flows of angle-multiplying maps.** / Tsujii, Masato.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 28, no. 1, pp. 291-317. https://doi.org/10.1017/S0143385707000430

}

TY - JOUR

T1 - Decay of correlations in suspension semi-flows of angle-multiplying maps

AU - Tsujii, Masato

PY - 2008/2/1

Y1 - 2008/2/1

N2 - We consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the PerronFrobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the PerronFrobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

AB - We consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the PerronFrobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the PerronFrobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

UR - http://www.scopus.com/inward/record.url?scp=38149062939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149062939&partnerID=8YFLogxK

U2 - 10.1017/S0143385707000430

DO - 10.1017/S0143385707000430

M3 - Article

AN - SCOPUS:38149062939

VL - 28

SP - 291

EP - 317

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 1

ER -