Boundary distance, lens maps and entropy of geodesic flows of Finsler metrics

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)469-490
Number of pages22
JournalGeometry and Topology
Volume20
Issue number1
DOIs
StatePublished - Feb 29 2016

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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