Related papers: Singularity patterns and dynamical degrees

Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…

Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…

A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several model systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Its order-by-order…

This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…

We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian…

We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…

We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…

This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…

We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…

For a dynamical map $\Lambda(t,0)$, which sends a state $\rho(0)$ of quantum open system to a state $\rho(t)=\Lambda(t,0)\rho(0)$, the decomposition law $\Lambda(t,0)=\Lambda(t,t_c)\Lambda(t_c,0)$ may break down at a specific time $t_c$. In…

We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…

We consider the parameterization ${\mathbf{f}}=(f_0,f_1,f_2)$ of a plane rational curve $C$ of degree $n$, and we want to study the singularities of $C$ via such parameterization. We do this by using the projection from the rational normal…

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…

A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…

Extropy, a complementary dual of entropy, (proposed by Lad et al. \cite{lad2015extropy} in 2015) has attracted considerable interest from the research community. In this study, we focus on discrete random variables and define conditional…

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form…

We propose some class of statistics suitable for estimation of the Hurst index of the fractional Brownian motion based on the second order increments of an observed discrete trajectory.

We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new…