Related papers: Stieltjes differential systems with non monotonic …
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…
We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
In this article, we study the local behaviour of the multiple zeta functions at integer points and write down a Laurent type expansion of the multiple zeta functions around these points. Such an expansion involves a convergent power series…
In this article we consider the general problem of translating definitions and results from the category of discrete-time dynamical systems to the category of flows. We consider the dynamics of homeomorphisms and flows on compact metric…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…
This work is devoted to the mathematical analysis of Stieltjes Bochner spaces and their applications to the resolution of a parabolic equation with Stieltjes time derivative. This novel formulation allows us to study parabolic equations…
The generating function of Stieltjes-Carlitz polynomials is a solution of Heun's differential equation and using this relation Carlitz was the first to get exact closed forms for some Heun functions. Similarly the associated…
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…
The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to…
This paper studies conditions for invariance of dynamical systems on stratified do- mains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We prove an inequality of the Lo\'{e}ve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes…
Our work studies sequences of orthogonal polynomials $ \{P_{n}(x)\}_{n=0}^{\infty} $ of the Laguerre-Hahn class, whose Stieltjes functions satisfy a Riccati type differential equation with polynomial coefficients, are subject to a…
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…