We develop a general compactification framework to facilitate analysis of nonautonomous
ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the …

Poincaré compactification is very important to investigate the dynamics of vector fields in the
neighborhood of the infinity, which is the main concern on the escape of particles to infinity …

Our purpose in this paper is to understand the geometry of the Poincaré compactification
and to apply this technique to prove that there exists a Poincaré compactification of vector …

In this paper, we study the Poincar\'e compactification of the limiting planar semiflow of a
coupled PDE-ODE system composed by a reaction-diffusion equation with large diffusion …

In this paper, the behavior of dynamics 'at infinity'of a four-dimensional autonomous food
web system has been investigated. For this, a topological method has been developed to …

In this work a theorical framework to apply the Poincaré compactification technique to locally
Lipschitz continuous vector fields is developed. It is proved that these vectors fields are …

We give a complete study of the dynamics of an infinitesimal mass under the Newtonian
attraction of two point masses---particles which escape along a line with zero energy---and a …

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In this work a theorical framework to apply the Poincaré compactification technique to locally
Lipschitz continuous vector fields is developed. It is proved that these vectors fields are …

Let X be the Hamiltonian vector field with two degrees of freedom associated to the cubic
polynomial Hamiltonian H (x, y, z, w). Using the Poincaré compactification we show that all …