2015/05/11 by Fernando Micena, Micena, F.
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1505.02662
openalex publication_date 2015/05/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this paper we focused our study on Derived From Anosov diffeomorphisms (DA diffeomorphisms ) of the torus \mathbbT3, it is, an absolute partially hyperbolic diffeomorphism on \mathbbT3 homotopic to an Anosov linear automorphism of the \mathbbT3. We can prove that if f: \mathbbT3 → \mathbbT3 is a volume preserving DA diffeomorphism homotopic to linear Anosov A, such that the center Lyapunov exponent satisfies λcf(x) > λcA > 0, with x belongs to a positive volume set, then the center foliation of f is non absolutely continuous. We construct a new open class U of non Anosov and volume preserving DA diffeomorphisms, satisfying the property λcf(x) > λcA > 0 for m-almost everywhere x ∈ \mathbbT3. Particularly for every f ∈ U, the center foliation of f is non absolutely continuous.