The asymptotic behavior of geodesic circles in 2-torus of revolution and a sub-ergodic property
type: Item
instance of: scholarly article
title: The asymptotic behavior of geodesic circles in 2-torus of revolution and a sub-ergodic property
zbMATH Open document ID: 1269.53038
author: Nobuhiro Innami
published in: Nihonkai Mathematical Journal
publication date: 2013-03-26T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.nihmj/1352124687
review text: Poincaré recurrence implies that on a complete Riemannian manifold \(M\) with finite volume, given points \(p,q\in M\), there are sequences of unit vectors \(x_n\in SM\) and times \(t_n\to+\infty\) such that the footpoints of \(x_n\) converge to \(p\) and \(\gamma_{x_n}(t_n)\to q\), where \(\gamma_x\) is the geodesic with initial condition \(\dot\gamma_x(0)=x\). This motivates the author to study similar recurrence properties for the geodesic flow of manifolds with finite volume, particularly tori. Such properties are related to the existence of poles (points at which the exponential map is surjective) and ergodicity of the geodesic flow.
reviewed by: Renato G. Bettiol
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58E10
zbMATH DE Number: 6148891
zbMATH Keywords: geodesic flow
zbMATH Keywords: Poincaré recurrence
zbMATH Keywords: billiard
zbMATH Keywords: pole
zbMATH Keywords: torus
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6148891