### Abstract

Let f be a sufficiently expanding C^{2} circle map. We prove that a certain Markov approximation scheme based on a partition of S^{1} into 2^{N} equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2^{-N}; C is a constant depending only on the map f.

Original language | English (US) |
---|---|

Pages (from-to) | 27-46 |

Number of pages | 20 |

Journal | Nonlinearity |

Volume | 11 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1998 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Nonlinearity*,

*11*(1), 27-46. https://doi.org/10.1088/0951-7715/11/1/004

**Computing invariant measures for expanding circle maps.** / Keane, Michael; Murray, Rua; Young, Lai Sang.

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 11, no. 1, pp. 27-46. https://doi.org/10.1088/0951-7715/11/1/004

}

TY - JOUR

T1 - Computing invariant measures for expanding circle maps

AU - Keane, Michael

AU - Murray, Rua

AU - Young, Lai Sang

PY - 1998/1

Y1 - 1998/1

N2 - Let f be a sufficiently expanding C2 circle map. We prove that a certain Markov approximation scheme based on a partition of S1 into 2N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2-N; C is a constant depending only on the map f.

AB - Let f be a sufficiently expanding C2 circle map. We prove that a certain Markov approximation scheme based on a partition of S1 into 2N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2-N; C is a constant depending only on the map f.

UR - http://www.scopus.com/inward/record.url?scp=0039758080&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039758080&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/11/1/004

DO - 10.1088/0951-7715/11/1/004

M3 - Article

VL - 11

SP - 27

EP - 46

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 1

ER -