The conference HAMSYS2018, continuation of the conference HAMSYS2014 celebrated inside the research program on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics.
In 1991 started the series of the HAMSYS Symposia. These symposia brought together top researches from several countries, working mainly in Hamiltonian Systems and Celestial Mechanics, as well as many graduate students who had the opportunity to learn from and connect with the experts in the field.
The VIII-th HAMSYS Symposium, denoted HAMSYS-2018, will take place at CRM (Centre de Recerca Matemàtica, at Universitat Autònoma de Barcelona). The emphasis of the talks will be on Hamiltonian dynamics and its relationship to several aspects of mechanics, geometric mechanics, and dynamical systems in general.
-Guanajuato, Mexico, September 30 - October 4, 1991
-Cocoyoc, Mexico, September 13-17, 1994
-Pátzcuaro, Mexico, December 7-11, 1998
-Guanajuato, Mexico, March 19-24, 2001
-Guanajuato, Mexico, July 7-11, 2008
-Ciudad de México, Mexico, November 29 - December 3, 2010
-Centre de Recerca Matemàtica, Bellaterra, June 2-6, 2014
The HAMSYS2018 will be mainly dedicated to the following topics:
The study of the dynamics of n point masses interacting according to Newtonian gravity is usually called the n-body problem. It can be considered as old as the history of the science and has influenced most of the areas in mathematics. However, most of the problems in Celestial Mechanics are beyond the present limits of the knowledge and many natural questions are difficult or impossible to solve when the number of bodies n is larger than 2.
In order to make progress against such complexity one must look for specific objects. From a geometrical point of view a key point consists in trying to understand the structure of the phase space looking for the equilibrium points, periodic orbits, invariant tori, ... The stable and unstable manifolds associated to these objects form a kind of network of connections, which together with the previous invariants objects constitute a big part of the main skeleton of the system.
One of the main ingredients of the phase space are the periodic orbits. Over the years, many authors have contributed to study the periodic orbits of a wide variety of n-body problems from different points of view. A particular interesting type of periodic orbit in the planar n-body problem is one in which the particles remain in the same shape relative to one another. The possible configurations for the particles in such orbits are called central configurations.