scholarly journals Avoiding early closing: ‘Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems’ – CORRIGENDUM

2010 ◽  
Vol 31 (4) ◽  
pp. 1269-1272
Author(s):  
RAFAEL DE LA LLAVE ◽  
ALISTAIR WINDSOR
Keyword(s):  
Diffeomorphism Groups ◽  
Anosov Systems ◽  
Conformal Structures

scholarly journals Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems

2009 ◽  
Vol 30 (4) ◽  
pp. 1055-1100 ◽  
Author(s):  
RAFAEL DE LA LLAVE ◽  
ALISTAIR WINDSOR
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Lie Group ◽  
Compact Manifold ◽  
Nauk Sssr ◽  
Anosov Diffeomorphism ◽  
Diffeomorphism Groups ◽  
Akad Nauk Sssr ◽  
Anosov Systems ◽  
Conformal Structures

AbstractThe celebrated Livšic theorem [A. N. Livšic, Certain properties of the homology ofY-systems,Mat. Zametki 10(1971), 555–564; A. N. Livšic, Cohomology of dynamical systems,Izv. Akad. Nauk SSSR Ser. Mat. 36(1972), 1296–1320] states that given a manifoldM, a Lie groupG, a transitive Anosov diffeomorphismfonMand a Hölder functionη:M↦Gwhose range is sufficiently close to the identity, it is sufficient for the existence of ϕ:M↦Gsatisfyingη(x)=ϕ(f(x))ϕ(x)−1that a condition—obviously necessary—on the cocycle generated byηrestricted to periodic orbits is satisfied. In this paper we present a new proof of the main result. These methods allow us to treat cocycles taking values in the group of diffeomorphisms of a compact manifold. This has applications to rigidity theory. The localization procedure we develop can be applied to obtain some new results on the existence of conformal structures for Anosov systems.

scholarly journals On the regularity of integrable conformal structures invariant under Anosov systems

2005 ◽  
Vol 12 (3) ◽  
pp. 377-385
Author(s):  
Rafael De La Llave ◽  
◽  
Victoria Sadovskaya ◽  
Keyword(s):  
Anosov Systems ◽  
Conformal Structures

scholarly journals Dimension rigidity in conformal structures

2017 ◽  
Vol 308 ◽  
pp. 1127-1186 ◽  
Author(s):  
Tushar Das ◽  
David Simmons ◽  
Mariusz Urbański
Keyword(s):  
Conformal Structures

Centralizers of derived-from-Anosov systems on : rigidity versus triviality

2021 ◽  
pp. 1-25
Author(s):  
SHAOBO GAN ◽  
YI SHI ◽  
DISHENG XU ◽  
JINHUA ZHANG
Keyword(s):  
Linear Part ◽  
Anosov Systems ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphism

Abstract In this paper, we study the centralizer of a partially hyperbolic diffeomorphism on ${\mathbb T}^3$ which is homotopic to an Anosov automorphism, and we show that either its centralizer is virtually trivial or such diffeomorphism is smoothly conjugate to its linear part.

On isomorphic classical diffeomorphism groups, III

1995 ◽  
Vol 13 (2) ◽  
pp. 117-127 ◽  
Author(s):  
Augustin Banyaga ◽  
Andrew McInerney
Keyword(s):  
Diffeomorphism Groups
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