This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some ...

The paper presents a computer algebra package that facilitates Lie algebraic symbolic computations required in the solution of a variety of problems, such as the solution of right-invariant differential equations evolving ...

We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, ...

Polynomial vector fields X: R3→ R3 that have invariant algebraic surfaces of the form M={f(x,y)z-g(x,y)=0}are considered. We prove that trajectories of X on M are solutions of a constrained differential system having I= { ...

In this paper we study the action of planar birational transformations, also known as plane Cremona maps, on quadratic planar differential systems. We provide geometrical characterizations of when a quadratic system is ...

Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential ...

We study bounded operators defined in terms of the regular representations of the C*-algebra of an amenable, Hausdorff, second countable, locally compact groupoid endowed with a continuous 2-cocycle. We concentrate on ...

In this paper we give the normal form of all polynomial differential systems in R3 having a weighted homogeneous surface f= 0 as an invariant algebraic surface and characterize among these systems those having a Darboux ...

This article deals with the algebra of gH-differentiable interval-valued functions. Specifically, we give conditions for the gH-differentiability of the sum and the gH-difference of two gH-differentiable interval-valued ...

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, g circle times C[t, t(-1), u vertical bar u(2) = (t(2) - ...