Related papers: Absolutely Continuous Spectrum for Parabolic Flows…
In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the…
We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of…
Analysis of power spectrum profiles for various tagged particle quantities in bulk SPC/E water is used to demonstrate that variations in mobility associated with the diffusional anomaly are mirrored in the exponent of the \onebyf\ region.…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…
We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.
The spectral properties of disordered fully-connected graphs with a special type of the node-node interactions are investigated. The approximate analytical expression for the ensemble-averaged spectral density for the Hamiltonian defined on…
We show that there exists a suitable neighborhood of a constant curvature hyperbolic metric such that, for all initial data in this neighborhood, the corresponding solution to a normalized cross curvature flow exists for all time and…
Estimation of extreme value copulas is often required in situations where available data are sparse. Parametric methods may then be the preferred approach. A possible way of defining parametric families that are simple and, at the same…
In this paper, we study the structure of Birkhoff spectra for hyperbolic dynamical systems. Given a H\"older observable \(f\) on a basic set \(\Lambda\), we obtain the following results: First, we characterize when the Birkhoff spectrum of…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…
We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of…
We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows…
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
We analyze the long-time behavior of solutions to semilinear parabolic equations in Euclidean space that arise as gradient flows of an energy functional. We prove that, for general initial data (including data without compact support) the…
An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wavenumber $k$ is a constant…
We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite…