Convex but not Strictly Convex Central Configurations

2017 ◽  
Vol 30 (4) ◽  
pp. 1427-1438 ◽  
Author(s):  
Antonio Carlos Fernandes ◽  
Braulio Augusto Garcia ◽  
Luis Fernando Mello
Keyword(s):  
Central Configurations ◽  
Strictly Convex

scholarly journals Strictly convex central configurations of the planar five-body problem

2017 ◽  
Vol 370 (3) ◽  
pp. 1907-1924 ◽  
Author(s):  
Kuo-Chang Chen ◽  
Jun-Shian Hsiao
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Strictly Convex

scholarly journals Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs

2001 ◽  
Vol 15 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Luis A. Caffarelli ◽  
Mikhail Feldman ◽  
Robert J. McCann
Keyword(s):  
Transport Problem ◽  
Strictly Convex ◽  
Convex Costs

scholarly journals Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
B. Benhammouda ◽  
A. Mansur ◽  
M. Shoaib ◽  
I. Szücs-Csillik ◽  
D. Offin
Keyword(s):  
Cross Sections ◽  
Body Problem ◽  
Mass Parameter ◽  
Central Configurations ◽  
Continuous Family ◽  
Classical Action ◽  
Dynamical Aspect ◽  
Homographic Solutions ◽  
Four Body Problem ◽  
Current Article

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem.

scholarly journals On the lattice points on strictly convex surfaces

1976 ◽  
Vol 8 (3) ◽  
pp. 298-307 ◽  
Author(s):  
Bohuslav Divis
Keyword(s):  
Lattice Points ◽  
Convex Surfaces ◽  
Strictly Convex
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