Related papers: Normalizers of planar systems with known first int…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rossler system and…
This article aims at finding sufficient conditions for a family of meromorphic functions to be normal by involving partial sharing of sets with differential polynomials. Moreover, corresponding results for normal meromorphic functions are…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
We present the ideas behind an algorithm to compute normalizers of primitive groups with non-regular socle in polynomial time. We highlight a concept we developed called permutation morphisms and present timings for a partial implementation…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
We make explicit a larger structural phenomenon hidden behind the existence of normalizers in terms of existence of certain cartesian maps related to the kernel functor.
S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equilibrium and solve the center problem. Further, we construct a…
Normaliz is a program for solving linear systems of inequalities. In this paper we present the algorithms implemented in the program, starting with version 2.0.
We obtain condition for existence of a center for a cubic planar differential system, which can be considered as a polynomial subfamily of the generalized Riccati system. We also investigate bifurcations of small limit cycles from the…
We continue the study of the center problem for the ordinary differential equation $v'=\sum_{i=1}^{\infty}a_{i}(x)v^{i+1}$ started in our earlier papers. In this paper we present the highlights of the algebraic theory of centers.
For a large class of systems of o.d.e.'s which have first integrals, the method of arrays yields the following results: i) The first integrals $I$ can be found by solving systems of linear equations. ii) How the first integral $I$ responds…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
We study the existence of centers of planar autonomous system of the form $$(S) \quad \dot x=y,\qquad \dot y = -h(x) - g(x)y - f(x)y^2.$$ We are interested in the period function $T$ around a center 0. A sufficient condition for the…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.