A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis a discriminant criterion elaborated in paper. This enables one to pick up single parameter that makes it possible identify all feasible solution classes as well DS critical and singular points solutions. The integrability considered family established. Nine specific are id...

A standard use of shadowing lemmas in dynamical systems theory is to prove density of periodic points. When there is symmetry present it is natural to investigate the density of periodic points of a given symmetry. We obtain several results in this direction. As an application, we prove a result about compact group extensions of hyperbolic and nonuniformly hyperbolic dynamical systems.

In this manuscript we introduce some important concepts concerning dynamical systems theory. We devote special attention to studying differential equations from a dynamical systems viewpoint. The introduced concepts are illustrated by examples.

Previous research has interpreted the patterned relations produced from the spacetime interactions of squash players as a dynamical system. Importantly, the theoretical basis for pattern formation within dynamical systems is predicated upon the shared information exchanges among the parts that comprise them. Thus, the patterned dynamics of a squash rally are the supposed product of shared infor...

In this note, we present a few methods (Theorems 1, 2, and 3) from discrete dynamical systems theory of obtaining new functions Q(n) from the known ones so that the dividing formulas n|Q(n) hold.