Orbits of linear group actions, random walks on homogeneous spaces and toral automorphisms

被引：31

作者：

Guivarc'h, Y

Starkov, AN

机构：

[1] Inst Rech Math Rennes 1, F-35042 Rennes, France

[2] All Russian Inst Elect, Istra 143500, Moscow Region, Russia

[3] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 117234, Russia

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2004年 / 24卷

关键词：

D O I：

10.1017/S0143385703000440

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let V be a finite-dimensional vector space over R and let Gamma subset of GL(V) be a semigroup. We study the closed F-invariant subsets of V - {0} under the condition that the Zariski closure of Gamma is semi-simple. We use the results to show that, if Gamma subset of SL(R-d) acts on T-d by automorphisms, then the orbits of F are finite or dense.

引用

页码：767 / 802

页数：36

共 50 条

[41] Linear group actions with at most three orbits of the largest size
Cinarci, Burcu
Keller, Thomas Michael
MONATSHEFTE FUR MATHEMATIK, 2024, 203 (02): : 313 - 322
[42] RANDOM-WALKS ON HOMOGENEOUS SPACES OF FINITELY-GENERATED NILPOTENT GROUPS
HENNION, H
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (21): : 1241 - 1242
[43] RANDOM-WALKS ON HOMOGENEOUS SPACES OF NILPOTENT GROUPS HAVING FINITE GENERATION
HENNION, H
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1976, 34 (03): : 245 - 267
[44] Classification of linear actions of algebraic groups on spaces of homogeneous forms
Bibikov, P. V.
Lychagin, V. V.
DOKLADY MATHEMATICS, 2012, 85 (01) : 109 - 112
[45] Classification of linear actions of algebraic groups on spaces of homogeneous forms
P. V. Bibikov
V. V. Lychagin
Doklady Mathematics, 2012, 85 : 109 - 112
[46] A restriction on proper group actions on homogeneous spaces of reductive type
Bochenski, Maciej
Ogryzek, Marek
GEOMETRIAE DEDICATA, 2015, 178 (01) : 405 - 411
[47] A restriction on proper group actions on homogeneous spaces of reductive type
Maciej Bocheński
Marek Ogryzek
Geometriae Dedicata, 2015, 178 : 405 - 411
[48] PSEUDO-KAHLERIAN HOMOGENEOUS SPACES ADMITTING A REDUCTIVE TRANSITIVE GROUP OF AUTOMORPHISMS
DORFMEISTER, J
GUAN, ZD
MATHEMATISCHE ZEITSCHRIFT, 1992, 209 (01) : 89 - 100
[49] GROUPS OF AUTOMORPHISMS OF LIE-GROUPS - DENSITY PROPERTIES, BOUNDED ORBITS, AND HOMOGENEOUS SPACES OF FINITE VOLUME
GREENLEAF, FP
MOSKOWITZ, M
PACIFIC JOURNAL OF MATHEMATICS, 1980, 86 (01) : 59 - 87
[50] Linear Control Systems on Homogeneous Spaces of the Heisenberg Group
Da Silva, Adriano
Kizil, Eyup
Duman, Okan
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2023, 29 (04) : 2065 - 2086

← 1 2 3 4 5 →