s from the 16th International Congress on Circumpolar Health

In this paper, we consider the problem of determining exact number periodic orbits for polynomial planar flows. This is a variant Hilbert’s 16th problem. Using natural definition computability, show that noncomputable on one hand and, other hand, computable uniformly set all structurally stable systems defined unit disk. We also prove there family which does not have sharp upper bound its orb...

The well-known Hilbert’s 16th problem has remained unsolved since Hilbert proposed the 23 mathematical problems at the Second International Congress of Mathematics in 1900 [Hilbert, 1902]. Recently, a modern version of the second part of the 16th problem was formulated by Smale [1998], chosen as one of the 18 challenging mathematical problems for the 21st century. To be more specific, consider ...

We study the analogue of the infinitesimal 16th Hilbert problem in dimension zero. Lower and upper bounds for the number of the zeros of the corresponding Abelian integrals (which are algebraic functions) are found. We study the relation between the vanishing of an Abelian integral I(t) defined over Q and its arithmetic properties. Finally, we give necessary and sufficient conditions for an Abe...

Two classical problems on plane polynomial vector fields, Hilbert’s 16th problem about the maximal number of limit cycles in such a system and Poincaré’s center-focus problem about conditions for all trajectories around a critical point to be closed, can be naturally reformulated for the Abel differential equation y′ = p(x)y + q(x)y. Recently, the center conditions for the Abel equation have be...