Related papers: A characterization of normal forms for control sys…

Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy,…

We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in…

In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class…

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…

Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence. Such parametric instabilities are…

We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed…

This paper provides a compositional approach to Taylor expansion, in the setting of cartesian differential categories. Taylor expansion is captured here by a functor that generalizes the tangent bundle functor to higher order derivatives.…

This paper has two parts. We first survey recent efforts on the Bloom conjecture which still remains open in the case of complex dimension at least 4. Bloom's conjecture concerns the equivalence of three regular types. There is a more…

Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…

This paper is devoted to normal forms for x-flat control-affine systems with two inputs. We propose a general triangular normal form which contains several other normal forms discussed in the literature as special cases. We derive…

We present a general framework to study relativistic compound systems in a Hamiltonian formalism. This formalism is based on the explicitly covariant formulation of light-front dynamics, with a decomposition of the state vector in Fock…

In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…

The Wei-Norman technique allows to express the solution of a system of linear non-autonomous differential equations in terms of product of exponentials. In particular it enables to find a time-ordered product of exponentials by solving a…

In an infinite dimensional Hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields. We prove that one can construct by the…

In the first part of the present work we consider periodically or quasiperiodically forced systems of the form $(d/dt)x = \epsilon f(x,t \omega )$, where $\epsilon\ll 1$, $\omega\in\mathbb{R}^d$ is a nonresonant vector of frequencies and…

Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct…

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…