Related papers: A note on local integrability of differential syst…

In this paper, we present two classes of lopsided systems and discuss their analytic integrability. The analytic integrable conditions are obtained by using the method of inverse integrating factor and theory of rotated vector field. For…

In this paper, we explore the local geometry of dynamical systems $\dot{x}=F(x)$ with real time parameterization, where $F$ is holomorphic on connected open subsets of $\mathbb{C}\stackrel{\sim}{=}\mathbb{R}^2$. We describe the geometry of…

This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…

M.F. Singer [Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc. 333 (1992), 673--688] proved the equivalence between Liouvillian integrability and Darboux integrability for two dimensional polynomial differential…

A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable…

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of…

In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the…

In this paper we present a-posteriori KAM results for existence of $d$-dimensional isotropic invariant tori for $n$-DOF Hamiltonian systems with additional $n-d$ independent first integrals in involution. We carry out a covariant…

In this paper we investigate the fractional Poincar\'e inequality on unbounded domains. In the local case, Sandeep-Mancini showed that in the class of simply connected domains, Poincar\'e inequality holds if and only if the domain does not…

The radial index of a 1-form on a singular set is a generalization of the classical Poincar\'e-Hopf index. We consider different classes of closed semi-analytic sets in R^n that contain 0 in their singular locus and we relate the radial…

We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain,…

Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…

Prelle and Singer showed in 1983 that if a system of ordinary differential equations defined on a differential field $K$ has a first integral in an elementrary field extension $L$ of $K$, then it must have a first integral consisting of…

It is known that the Principal Poincar\'e Pontryagin Function is generically an Abelian integral. In non generic cases it is an iterated integral. In previous papers one of the authors gives a precise description of the Principal Poincar\'e…

Let $X$ be a connected space. An element $[f]\in \pi_n(X)$ is called rationally inert if $\pi_*(X)\otimes \mathbb Q \to \pi_*(X\cup_fD^{n+1})\otimes \mathbb Q$ is surjective. We extend the results obtained in the simply connected case, and…

The optimal lower or upper bounds for sums of the first $m$ eigenvalues of Sturm-Liouville operators can be obtained by solving the corresponding critical systems, which are Hamiltonian systems of $m$ degrees of freedom with $m$ parameters.…

In this paper, we investigate the continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system. By constructing a sequence approximate solutions and calculating the error terms, we show that the data-to-solution map…

The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…

Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix…

Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…