scholarly journals On the statistical stability of Lorenz attractors with a stable foliation

2018 ◽  
Vol 39 (12) ◽  
pp. 3169-3184 ◽  
Author(s):  
WAEL BAHSOUN ◽  
MARKS RUZIBOEV
Keyword(s):  
Stable Foliation ◽  
Statistical Stability ◽  
Lorenz Attractors

We prove statistical stability for a family of Lorenz attractors with a $C^{1+\unicode[STIX]{x1D6FC}}$ stable foliation.

scholarly journals Statistical stability of geometric Lorenz attractors

2014 ◽  
Vol 224 (3) ◽  
pp. 219-231 ◽  
Author(s):  
José F. Alves ◽  
Mohammad Soufi
Keyword(s):  
Statistical Stability ◽  
Lorenz Attractors

On the integrability of intermediate distributions for Anosov diffeomorphisms

1995 ◽  
Vol 15 (2) ◽  
pp. 317-331 ◽  
Author(s):  
M. Jiang ◽  
Ya B. Pesin ◽  
R. de la Llave
Keyword(s):  
Finite Number ◽  
Lyapunov Exponents ◽  
Periodic Orbits ◽  
Three Dimensional ◽  
Dimensional Torus ◽  
Anosov Diffeomorphism ◽  
Anosov Diffeomorphisms ◽  
Stable Foliation

AbstractWe study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

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