lattice actions
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2021 ◽  
pp. 1-51
Author(s):  
CHRIS CONNELL ◽  
THANG NGUYEN ◽  
RALF SPATZIER

Abstract This paper develops new techniques for studying smooth dynamical systems in the presence of a Carnot–Carathéodory metric. Principally, we employ the theory of Margulis and Mostow, Métivier, Mitchell, and Pansu on tangent cones to establish resonances between Lyapunov exponents. We apply these results in three different settings. First, we explore rigidity properties of smooth dominated splittings for Anosov diffeomorphisms and flows via associated smooth Carnot–Carathéodory metrics. Second, we obtain local rigidity properties of higher hyperbolic rank metrics in a neighborhood of a locally symmetric one. For the latter application we also prove structural stability of the Brin–Pesin asymptotic holonomy group for frame flows. Finally, we obtain local rigidity properties for uniform lattice actions on the ideal boundary of quaternionic and octonionic symmetric spaces.


2017 ◽  
Vol 186 (3) ◽  
pp. 913-972 ◽  
Author(s):  
Aaron Brown ◽  
Federico Rodriguez Hertz ◽  
Zhiren Wang

2014 ◽  
Vol 45 (4) ◽  
pp. 800-807 ◽  
Author(s):  
Alexey A. Vladimirov ◽  
Dmitri Diakonov
Keyword(s):  

2014 ◽  
Author(s):  
Wolfgang Bietenholz ◽  
Michael Boegli ◽  
Urs Gerber ◽  
Ferenc Niedermayer ◽  
Michele Pepe ◽  
...  

2013 ◽  
Vol 2013 (3) ◽  
Author(s):  
W. Bietenholz ◽  
M. Bögli ◽  
F. Niedermayer ◽  
M. Pepe ◽  
F. G. Rejón-Barrera ◽  
...  

2011 ◽  
Vol 157 (1) ◽  
pp. 1-21 ◽  
Author(s):  
François Maucourant ◽  
Barak Weiss
Keyword(s):  

2011 ◽  
Vol 85 (1) ◽  
pp. 129-134
Author(s):  
P. Hegdea ◽  
F. Karsch ◽  
E. Laermann ◽  
S. Scheredin
Keyword(s):  

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