### Abstract

We construct a kneading theory à la Milnor-Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters.

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

Pages (from-to) | 375-394 |

Number of pages | 20 |

Journal | Communications in Mathematical Physics |

Volume | 190 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1997 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Towards a kneading theory for Lozi mappings. II : Monotonicity of the topological entropy and Hausdorff dimension of attractors.** / Ishii, Yutaka.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Towards a kneading theory for Lozi mappings. II

T2 - Monotonicity of the topological entropy and Hausdorff dimension of attractors

AU - Ishii, Yutaka

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We construct a kneading theory à la Milnor-Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters.

AB - We construct a kneading theory à la Milnor-Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters.

UR - http://www.scopus.com/inward/record.url?scp=0031549916&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031549916&partnerID=8YFLogxK

U2 - 10.1007/s002200050245

DO - 10.1007/s002200050245

M3 - Article

AN - SCOPUS:0031549916

VL - 190

SP - 375

EP - 394

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -