Maxime Murray

Florida Atlantic University | FAU · Department of Mathematical Sciences

We develop computer assisted arguments for proving the existence of transverse homoclinic connecting orbits, and apply these arguments for a number of non-perturbative parameter and energy values in the spatial equilateral circular restricted four body problem. The idea is to formulate the desired connecting orbits as solutions of certain two point...

The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equi-lateral restricted four body problem admit certain simple homoclinic oribts which form the skeleton of the complete homoclinic intersection-or homoclinic web. In the present work the planar restricted four body problem is viewed as an invariant subsyste...

The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admit certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection -- or homoclinic web. In the present work, the planar restricted four-body problem is viewed as an invariant subsy...

This work is a translation from French of the memoir "Connaissance actuelle des orbites dans le problème des trois corps" written by Elis Strömgren in 1933 about his research at the Copenhagen observatory. This work is often referred to in contemporary works however it appears to be only available in French. This is a modest attempt by the authors...

This paper develops Chebyshev-Taylor spectral methods for studying stable/unstable manifoldsattached to periodic solutions of differential equations. The work exploits the parameterizationmethod – a general functional analytic framework for studying invariant manifolds. Useful fea-tures of the parameterization method include the fact that it can fo...

In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation $u""+\beta u" + e^u-1=0$ for all parameter values $\beta \in [0.5,1.9]$. For each $\beta$, a parameterization of the stable manifold is computed and the symmetric homoclinic orbits are obtained by solving a projected boundary value problem using Cheb...