GEODESIC FLOWS MODELED BY EXPANSIVE FLOWS: COMPACT SURFACES WITHOUT CONJUGATE POINTS AND CONTINUOUS GREEN BUNDLES

被引：3

作者：

Gelfert, Katrin ^{[1
]}

Ruggiero, Rafael O. ^{[2
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945909 Rio De Janeiro, Brazil

[2] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, Rua Marques de Sao Vicente 225, BR-22451900 Rio de Janeiro, RJ, Brazil

来源：

ANNALES DE L INSTITUT FOURIER | 2023年 / 73卷 / 06期

关键词：

Geodesic flows; conjugate points; expansive flow; Green bundles; measure of maximal entropy; RIEMANNIAN-MANIFOLDS; ENTROPY; SPECTRUM;

D O I：

10.5802/aif.3574

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the geodesic flow of a compact surface without conjugate points and genus greater than one and continuous Green bundles. Identifying each strip of bi-asymptotic geodesics induces an equivalence relation on the unit tangent bundle. Its quotient space is shown to carry the structure of a 3 -dimensional compact manifold. This manifold carries a canonically defined continuous flow which is expansive, time-preserving semi-conjugate to the geodesic flow, and has a local product structure. An essential step towards the proof of these properties is to study regularity properties of the horospherical foliations and to show that they are indeed tangent to the Green subbundles. As an application it is shown that the geodesic flow has a unique measure of maximal entropy.

引用

页码：2605 / 2649

页数：46

共 50 条

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