Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics

Let AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff¹(M) is a C¹-Anosov transitive diffeomorphisms and A is an SL(d,R) cocycle dominated with respect to f. We prove that open and densely in AC_D(M,SL(d,R)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure μ_f. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AutLeb(M) × L^p(M,SL(d,R)).     

Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations

Aequationes mathematicae - We consider $$3times 3$$ partially hyperbolic linear differential systems over an ergodic flow $$X^t$$ and derived from the linear homogeneous differential equation...     

Dynamics of generic 2-dimensional linear differential systems

We prove that for a C⁰-generic (a dense Gδ) subset of all the 2-dimensional conservative nonautonomous linear differential systems, either Lyapunov exponents are zero or there is a dominated splitting μ almost every point.     

Automated measurement of ultrasound velocity and attenuation

A fully-automated system has been developed to measure changes in ultrasonic velocity and the attenuation coefficient resulting from changes in temperature and magnetic field. Accuracy and sensitivity comparable to the pulse-echo overlap technique have been achieved together with an increase in temperature resolution and sample throughput as a result of the automation. All components of the instrumentation are commercially available.