Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHolder regularity for the spectrum of translation flows
56
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The paper is devoted to generic translation flows corresponding to Abelian differentials on flat surfaces of arbitrary genus $gge 2$. These flows are weakly mixing by the Avila-Forni theorem. In genus 2, the Holder property for the spectral measures of these flows was established in our papers [10,12]. Recently Forni [17], motivated by [10], obtained Holder estimates for spectral measures in the case of surfaces of arbitrary genus. Here we combine Fornis idea with the symbolic approach of [10] and prove Holder regularity for spectral measures of flows on random Markov compacta, in particular, for translation flows in all genera.
rate research
Read More
We prove the Holder continuity of the integrated density of states for a class of quasi-periodic long-range operators on $ell^2(Z^d)$ with large trigonometric polynomial potentials and Diophantine frequencies. Moreover, we give the Holder exponent in terms of the cardinality of the level sets of the potentials, which improves, in the perturbative regime, the result obtained by Goldstein and Schlag cite{gs2}. Our approach is a combination of Aubry duality, generalized Thouless formula and the regularity of the Lyapunov exponents of analytic quasi-periodic $GL(m,C)$ cocycles which is proved by quantitative almost reducibility method.
We provide an abstract framework for the study of certain spectral properties of parabolic systems; specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive certain spectral results for skew products over translations and Furstenberg transformations.
We consider a class of nonautonomous elliptic operators ${mathscr A}$ with unbounded coefficients defined in $[0,T]timesR^N$ and we prove optimal Schauder estimates for the solution to the parabolic Cauchy problem $D_tu={mathscr A}u+f$, $u(0,cdot)=g$.
This paper proves Holder continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first shows that viscosity solutions to certain nonlinear ordinary differential equations involving the generalized fractional time derivative are Holder continuous.
We prove the Holder continuity of the Lyapunov exponent for quasi-periodic Schrodinger cocycles with a $C^2$ cos-type potential and any fixed Liouvillean frequency, provided the coupling constant is sufficiently large. Moreover, the Holder exponent is independent of the frequency and the coupling constant.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
