Publicación: N-BODY DYNAMICS ON AN INFINITE CYLINDER: THE TOPOLOGICAL SIGNATURE IN THE DYNAMICS
Fecha
2020
Autores
Título de la revista
ISSN de la revista
Título del volumen
Editor
REGULAR & CHAOTIC DYNAMICS
Resumen
THE FORMULATION OF THE DYNAMICS OF N-BODIES ON THE SURFACE OF AN INFINITE CYLINDER IS CONSIDERED. WE HAVE CHOSEN SUCH A SURFACE TO BE ABLE TO STUDY THE IMPACT OF THE SURFACE?S TOPOLOGY IN THE PARTICLE?S DYNAMICS. FOR THIS PURPOSE WE NEED TO MAKE A CHOICE OF HOW TO GENERALIZE THE NOTION OF GRAVITATIONAL POTENTIAL ON A GENERAL MANIFOLD. FOLLOWING BOATTO, DRITSCHEL AND SCHAEFER [5], WE DEFINE A GRAVITATIONAL POTENTIAL AS AN ATTRACTIVE CENTRAL FORCE WHICH OBEYS MAXWELL?S LIKE FORMULAS.
AS A RESULT OF OUR THEORETICAL DIFFERENTIAL GALOIS THEORY AND NUMERICAL STUDY ? POINCARÉ SECTIONS, WE PROVE THAT THE TWO-BODY DYNAMICS IS NOT INTEGRABLE. MOREOVER, FOR VERY LOW ENERGIES, WHEN THE BODIES ARE RESTRICTED TO A SMALL REGION, THE TOPOLOGICAL SIGNATURE OF THE CYLINDER IS STILL PRESENT IN THE DYNAMICS. A PERTURBATIVE EXPANSION IS DERIVED FOR THE FORCE BETWEEN THE TWO BODIES. SUCH A FORCE CAN BE VIEWED AS THE PLANAR LIMIT PLUS THE TOPOLOGICAL PERTURBATION. FINALLY, A POLYGONAL CONFIGURATION OF IDENTICAL MASSES (IDENTICAL CHARGES OR IDENTICAL VORTICES) IS PROVED TO BE AN UNSTABLE RELATIVE EQUILIBRIUM FOR ALL N > 2.
