## Abstract

By using the cycle expansion, we obtain general expressions for the determination of the diffusion coefficient D of a piecewise linear map which is parametrized by k and h (where the map contains 2k+5 branches of line segment, and h is the height of the shortest line). By restricting h=β/m [β=1,...,(k+1)/2; m is the slope of the map], a closed form expression of D can be obtained and some of its consequences are discussed. The limiting form of D (k→) is then shown to be k2. For the simplest case with k=1, we also show that more exact results can be found. A limiting case with h→0 is discussed where agreement with the result obtained from the invariant measure approach is established.

Original language | English |
---|---|

Pages (from-to) | 2815-2822 |

Number of pages | 8 |

Journal | Physical Review E |

Volume | 51 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)