相关论文: On the algebraic non-integrability of the Halphen …

In this paper we construct a new completely integrable system. This system is an instance of a master system of differential equations in $5$ unknowns having $3$ quartics constants of motion.We find via the Painlev\'e analysis the principal…

We prove that the motion of a triaxial Riemann ellipsoid of homogeneous liquid without angular momentum does not possess an additional first integral which is meromorphic in position, impulsions, and the elliptic functions which appear in…

Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…

Except for a limited number of cases, a complete classification of the Diophantine sets of polynomial rings and fields of rational functions seems out of reach at present. We contribute to this problem by proving that several natural sets…

In this manuscript we develop a new technique for showing that a nonlinear algebraic differential equation is strongly minimal based on the recently developed notion of the degree of nonminimality of Freitag and Moosa. Our techniques are…

We show that the special unitary group associated to an involution of the second kind on a central division algebra of degree three does not contain hermitian or skew-hermitian elements. Especially, there are no reflections. For Albert's…

The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.

We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…

We prove that general three- or four-dimensional systems %of differential equations are real-analytically nonintegrable near degenerate equilibria in the Bogoyavlenskij sense under additional weak conditions when the Jacobian matrices have…

We present a universal construction of Diophantine equations with bounded complexity in Isabelle/HOL. This is a formalization of our own work in number theory. Hilbert's Tenth Problem was answered negatively by Yuri Matiyasevich, who showed…

In this paper, we generalized the known Laplace-transform final-value theorem. From our conclusion, one can deduce the existing results in [1, 3, 12]. By using final value theorem, we give a new proof that Caputo fractional differential…

We prove that there are no bounded domains with smooth boundaries in even-dimensional Euclidean spaces, such that the volumes cut off from them by affine hyperplanes depend algebraically on these hyperplanes. For convex ovals in $R^2$, this…

A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting…

In this article, using only elementary knowledge of complex numbers, we sketch a proof of the celebrated Abel--Ruffini theorem, which states that the general solution to an algebraic equation of degree five or more cannot be written using…

We show that for $n \geq 2$ there exist real analytic Hamiltonian systems on $\mathbf{R}^{2n}$ with non-resonant eigenvalues at a singular point, of which the Birkhoff normal form itself is divergent. The proof of the result is achieved by…

It is proved that the non-rationality of a generic cubic fourfold follows from a conjecture on the non-decomposability in the direct sum of non-trivial polarized Hodge structures of the polarized Hodge structure on transcendental cycles on…

We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we…

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…

We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have established solid theoretical basis through a relation between the…

In this paper we prove the nonexistence of nontrivial solution to \begin{equation*} \begin{cases} -\Delta u =f(u) &\text{in }\Omega, \\ u=0 &\text{on } \partial \Omega, \end{cases} \end{equation*} being $\Omega \subset \mathbb{R}^N$ ($N\in…