## Abstract

We show that a small perturbation of the boundary distance function of a simple Finsler metric on the n -disc is also the boundary distance function of some Finsler metric. (Simple metrics form an open class containing all flat metrics.) The lens map is a map that sends the exit vector to the entry vector as a geodesic crosses the disc. We show that a small perturbation of a lens map of a simple Finsler metric is in its turn the lens map of some Finsler metric. We use this result to construct a smooth perturbation of the metric on the standard 4-dimensional sphere to produce positive metric entropy of the geodesic flow. Furthermore, this flow exhibits local generation of metric entropy; that is, positive entropy is generated in arbitrarily small tubes around one trajectory.

Original language | English (US) |
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Pages (from-to) | 469-490 |

Number of pages | 22 |

Journal | Geometry and Topology |

Volume | 20 |

Issue number | 1 |

DOIs | |

State | Published - Feb 29 2016 |

## All Science Journal Classification (ASJC) codes

- Geometry and Topology