Mono-atomic disintegration and Lyapunov exponents for derived from\n Anosov diffeomorphisms

2013/05/07 by Gabriel Ponce, Ponce, Gabriel, Régis Varão +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Lipid Membrane Structure and Behavior #Mathematical Dynamics and Fractals #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.1305.1588

openalex publication_date 2013/05/07 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

In this paper we mainly address the problem of disintegration of Lebesgue\nmeasure and measure of maximal entropy along the central foliation of\n(conservative) Derived from Anosov (DA) diffeomorphisms. We prove that for\naccessible DA diffeomorphisms of mathbbT³, atomic disintegration has the\npeculiarity of being mono-atomic (one atom per leaf). We further provide open\nand non-empty condition for the existence of atomic disintegration. Finally, we\nprove some new relations between Lyapunov exponents of DA diffeomorphisms and\ntheir linearization.\n

Citations

• Ergodicity and partial hyperbolicity on the 3-torus

Related

• A relation between entropy and transitivity of Anosov diffeomorphisms
• Extended flexibility of Lyapunov exponents for Anosov diffeomorphisms
• Measures of maximal entropy that are SRB
• On Anosov diffeomorphisms with asymptotically conformal periodic data
• Flexibility of Lyapunov exponents with respect to two classes of measures on the torus