Related papers: Computing covariant Lyapunov vectors in Hilbert sp…
Consider a $C^1$ vector field together with an ergodic invariant probability that has $\ell$ nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of $\ell$ differential…
Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Cl(p,q) are presented for n=p+q=3. The obtained exponential formulas were applied to find exact GA trigonometric and…
In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and $\Phi^4$ models. In this case, characteristic (also called…
Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a…
We propose a method for the calculation of vacuum expectation values (VEVs) given a non-trivial, long-distance vacuum wave functional (VWF) of the kind that arises, for example, in variational calculations. The VEV is written in terms of a…
We analyse the Krylov solvability of inverse linear problems on Hilbert space $\mathcal{H}$ where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound…
We study linear co-cycles in GL(d,R) (or C) depending on a parameter (in a Lipschitz or Holder fashion) and establish Holder regularity of the Lyapunov exponents for the shift dynamics on the base. We also obtain rates of convergence of the…
Dilated convolutions are widely used in deep semantic segmentation models as they can enlarge the filters' receptive field without adding additional weights nor sacrificing spatial resolution. However, as dilated convolutional filters do…
The exact form of the Jacobi -- Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold M_E = {q in R^N | V(q) < E} of a standard Hamiltonian system, equipped…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…
We employ an isometry group invariants approach to study Killing tensors of valence three defined in the Euclidean plane. The corresponding invariants are found to be homogeneous polynomials of the parameters of the vector space of the…
In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove the convergence of the conjugate gradient iterates to an exact solution to the inverse problem in the most general case where the self-adjoint,…
We consider an abstract space of measurable linear cocycles and we assume the availability in this space of some appropriate uniform large deviation type estimates. Under these hypotheses we establish the continuity of the Oseledets…
The celebrated Oseledets theorem \cite{O}, building over seminal works of Furstenberg and Kesten on random products of matrices and random variables taking values on non-compact semisimple Lie groups \cite{FK,Furstenberg}, ensures that the…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…
Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for…
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…