2018
DOI: 10.1007/s11856-018-1787-9
|View full text |Cite
|
Sign up to set email alerts
|

Some ergodic and rigidity properties of discrete Heisenberg group actions

Abstract: The goal of this paper is to study ergodic and rigidity properties of smooth actions of the discrete Heisenberg group H. We establish the decomposition of the tangent space of any C ∞ compact Riemannian manifold M for Lyapunov exponents, and show that all Lyapunov exponents for the center elements are zero. We obtain that if an H group action contains an Anosov element, then under certain conditions on the element, the center elements are of finite order. In particular there is no faithful codimensional one An… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
4
0

Year Published

2020
2020
2025
2025

Publication Types

Select...
4
1

Relationship

0
5

Authors

Journals

citations
Cited by 5 publications
(4 citation statements)
references
References 21 publications
0
4
0
Order By: Relevance
“…This is precisely the structural stability result described in Example 2 of [8]. Now we present an application to the rigidity of discrete Heisenberg group actions on compact manifolds [11]. The discrete Heisenberg group is the unique group H generated by three elements a, b, c satisfying ac = ca, bc = cb and ab = bac.…”
mentioning
confidence: 65%
See 2 more Smart Citations
“…This is precisely the structural stability result described in Example 2 of [8]. Now we present an application to the rigidity of discrete Heisenberg group actions on compact manifolds [11]. The discrete Heisenberg group is the unique group H generated by three elements a, b, c satisfying ac = ca, bc = cb and ab = bac.…”
mentioning
confidence: 65%
“…Since H is nilpotent, and the Anosov diffeomorphisms have the shadowing property, we can combine lemmas 2.12 and 2.13 in [5] to obtain that T has the shadowing property too. It then follows from Corollary 1.9 that T is rigid (or C 1,1,0 locally rigid in [11]'s terminology). This represents a rigidity result of the discrete Heisenberg group actions on tori (see also Theorem E in [11]).…”
mentioning
confidence: 96%
See 1 more Smart Citation
“…) is distorted in the word metric. When the Heisenberg group G A acts on a C ∞ compact Riemannian manifold, Hu-Shi-Wang [36] proves that the topological entropy and all Lyapunov exponents of the central element are zero. These results are special cases of Theorem 0.1 and Corollary 0.2, by choosing special length functions.…”
Section: Introductionmentioning
confidence: 99%