Fuchsian groups from the dynamical viewpoint
type: Item
instance of: scholarly article
title: Fuchsian groups from the dynamical viewpoint
zbMATH Open document ID: 0986.37033
DOI: 10.1007/BF02269378
author: A. N. Starkov
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: This paper provides an elementary introduction to Fuchsian groups theory for specialists on dynamical systems. The author paid special attention to the structure of orbits of the horocycle flow on \(T^1M\) of the corresponding hyperbolic surface \(M=\Gamma\setminus\Delta\), where \(\Gamma\) is the Fuchsian group. He constructs Fuchsian groups with new types of horocycle orbits which are neither closed nor dense in the nonwandering set. Moreover, the author presents both a unique classification of Fuchsian groups from the dynamical point of view and some open problems.
Mathematics Subject Classification ID: 37F30
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 1431794
zbMATH Keywords: Fuchsian group
zbMATH Keywords: horocycle flow
zbMATH Keywords: nonwandering set
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3310101
cites work: Horocycle flow on geometrically finite surfaces
cites work: Q4274267
cites work: Compactness of minimal closed invariant sets of actions of unipotent groups
cites work: Q3993094
cites work: On the Green's function of Fuchsian groups
cites work: On Fuchsian groups of accessible type
cites work: Q3923301
cites work: Q4743476
cites work: Examples of discrete groups of hyperbolic motions conservative but not ergodic at infinity
cites work: A rigidity theorem for Möbius groups
full work available at URL: https://doi.org/10.1007/bf02269378
OpenAlex ID: W1970380018
description: scientific article; zbMATH DE number 1431794