The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank

2005 ◽  
Vol 149 (1) ◽  
pp. 171-183 ◽  
Author(s):  
Gerhard Knieper
Keyword(s):  
Symmetric Spaces ◽  
Geodesic Flows ◽  
Maximal Measure ◽  
Higher Rank

The spectrum and heat dynamics of locally symmetric spaces of higher rank

2014 ◽  
Vol 35 (5) ◽  
pp. 1524-1545 ◽  
Author(s):  
LIZHEN JI ◽  
ANDREAS WEBER
Keyword(s):  
Symmetric Spaces ◽  
Chaotic Behavior ◽  
Heat Semigroup ◽  
Locally Symmetric Spaces ◽  
Rank One ◽  
Higher Rank

The aim of this paper is to study the spectrum of the$L^{p}$Laplacian and the dynamics of the$L^{p}$heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the$L^{p}$heat semigroup on$M$has a certain chaotic behavior if$p\in (1,2)$, whereas for$p\geq 2$such chaotic behavior never occurs.

Sign in / Sign up

Export Citation Format

Share Document