|
|||||
|
|
Continuation of normal doubly symmetric orbits in conservative reversible systems |
|
| Authors: | Francisco Javier Muñoz-Almaraz Emilio Freire Jorge Galan-Vioque Andre Vanderbauwhede |
| Institution: | (1) Departamento de Ciencias Físicas, Matemáticas y de la Computación, Universidad Cardenal Herrera-CEU, 46115 Alfara del Patriarca, Spain;(2) Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros de Sevilla, Camino de los Descubrimientos s/n, Sevilla, 41092, Spain;(3) Department of Pure Mathematics and Computer Algebra, University of Gent, Krijgslaan 281, B-9000 Gent, Belgium |
| Abstract: | In this paper we introduce the concept of a quasi-submersive mapping between two finite-dimensional spaces, we obtain the main properties of such mappings, and we introduce “normality conditions” under which a particular class of so-called “constrained mappings” are quasi-submersive at their zeros. Our main application is concerned with the continuation properties of normal doubly symmetric orbits in time-reversible systems with one or more first integrals. As examples we study the continuation of the figure-eight and the supereight choreographies in the N-body problem. |
| Keywords: | Hamiltonian and conservative systems Time-reversibility Normal doubly symmetric solutions Periodic solutions Numerical continuation Boundary value problem N-body problem |
| 本文献已被 SpringerLink 等数据库收录！ | |