Related papers: Extension, embedding and global stability in two d…
Using the in-in formalism, we generalize the recently constructed magnetoelastic EFT arXiv:2112.13873 [hep-th] to describe the damping dynamics of ferromagnetic systems at long wavelengths. We find that the standard Gilbert damping term…
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
Matrix measures induced by vector norms are widely used in contraction theory of nonlinear dynamical systems. A natural and important robustness question is whether negativity of a matrix measure is preserved under arbitrary nonnegative…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
It is often of interest to know which systems will approach a periodic trajectory when given a periodic input. Results are available for certain classes of systems, such as contracting systems, showing that they always entrain to periodic…
Let $(X,\left\Vert \cdot \right\Vert )$ be a real normed space of dimension $N\in \mathbb{N}$ with a basis $(e_{i})_{1}^{N}$ such that the norm is invariant under coordinate permutations. Assume for simplicity that the basis constant is at…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it…
Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…
We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry…
A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
In two recent papers we introduced some new techniques for constructing an extension of a probability-preserving system $T:\mathbb{Z}^d\curvearrowright (X,\mu)$ that enjoys certain desirable properties in connexion with the asymptotic…
We present a canonical extension of topological dynamics to transfinite iterations, which makes precise the idea of dynamical phenomena stabilizing at different time-scales. Specifically, consider a sequence of self-maps $F=\{f_n\}$ of a…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…