scholarly journals Measures on the geometric limit set in higher rank symmetric spaces

2004 ◽  
Vol 22 ◽  
pp. 59-69
Author(s):  
Gabriele Link
Keyword(s):  
Symmetric Spaces ◽  
Limit Set ◽  
Geometric Limit ◽  
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.

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