Remote limit points on surfaces
type: Item
instance of: scholarly article
title: Remote limit points on surfaces
zbMATH Open document ID: 1013.37009
DOI: 10.1016/S0022-0396(02)00065-7
author: M. H. Vanderschoot
author: Nelson G. Markley
published in: Journal of Differential Equations
publication date: 2003-04-02T00:00:00Z
review text: The authors study the omega limit sets of orbits of a flow on a compact surface \(M\) of genus at least 2. The flow on \(M\) lifts to the universal covering \(\widetilde{M}\) of \(M\). The orbits studied are those with lifts to \(\widetilde{M}\) that limit to a fixed point \(a\in \mathbb{K}\) of a covering transformation \(T\). The circle orthogonal to \(\mathbb{K}\) determined by the fixed points \(a\) and \(b\) of \(T\) is called the axis of \(T\). The remote limit points are the points in the omega limit set arising from the sequences of points on the positive orbit for which the hyperbolic distance of the lift to the axis of \(T\) goes to infinity. The main result about these remote limit points is that they must be fixed points.
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1891268
zbMATH Keywords: omega limit sets
zbMATH Keywords: sections
zbMATH Keywords: universal covering
zbMATH Keywords: Hausdorff metric
reviewed by: Klaudiusz Wójcik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891268