Navigate Up
Sign In
  • CRM
  • CRM
  • CRM
CRM > English > Activities > Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics (DANCE Winter School)
Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics (DANCE Winter School)
Basic and last minute information

Dates: January 27 to 31, 2014                                                                        GROUP PICTURE AND PHOTO GALLERY

Timetable​ (NOTES POSTED HERE​​​)


The Advanced course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics is a joint activity of the DANCE (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad) Spanish network with with the CRM in the framework of the research programme Central Configurations, periodic orbits and Beyond.

It is the 11th winter school in Dynamical Systems of the DANCE network.

This series of winter schools aims at training their participants both theoretically and in applications in the field of the nonlinear science; with the aim that theory and applications enforce each other. This will be done in an atmosphere of informal discussion, interchange of ideas and critical discussion of results. Attention will be paid to the numerical and computational issues.

These winter schools should help the basic training of young researchers, whilst opening new fields for senior ones. As a byproduct, the courses are planned to receive official recognition in some doctorate programs. There will be a number of partial and full accommodation grants for young participants.


Montserrat Corbera (Universitat de Vic)
Josep Maria Cors (Universitat Politècnica de Catalunya)

Jaume Llibre (Universitat Autònoma de Barcel
Enrique Ponce (Universidad de Sevilla)


Richard Moeckel
Title: Central Configurations of the Newtonian N-Body Problem
A central configuration is a special arrangement of N point masses such that the gravitational acceleration vector of each mass due to the other masses is proportional to its position vector relative to the center of mass. The first examples of central configurations date to the 18th century investigations of Euler and Lagrange. Since then, they have played an important role in the qualitative study of the dynamics. In addition to providing simple periodic solutions, they are relevant for studies of collision, scattering to infinity and bifurcation of the integral manifolds.
This course will cover some of these applications and then focus on methods for studying central configurations for their own sake. We will focus on questions of existence and enumeration of various types of central configurations, including algebraic-geometrical approaches to Smale’s 6th problem: Is the number of central configurations always finite?
Carles Simó
Title: Dynamical properties in Hamiltonian Systems
Objective: To describe the main mechanisms leading to a fairly global description of the dynamics in conservative systems.
1. Basic symplectic 2D maps. Return maps, standard, separatrix and H\'enon maps. Invariant curves, invariant manifolds, splitting of
    separatrices, invariant Cantor sets, creation of chaos, Lyapunov exponents. Measure problems. Basic theoretical results and
    computational methods.
2. Some key theoretical results: averaging theory under periodic and quasi-periodic excitation; normal forms, convergence problems and
    Gevrey properties; KAM theory; Nekhorosev theory, stable/unstable/centre manifolds.
3. Symbolic and numeric tools for the computation of periodic and quasi-periodic solutions and invariant manifolds.
4. Applications: Global behavior of orbits near the libration points in the RTBP; some problems and subproblems of the general 3-body
    system. Escape, capture and diffusion.

Jaume Llibre
Title: Periodic solutions via averaging theory
The goal of these lectures is to study the periodic solutions of autonomous differential systems in R^n via the averaging theory.
This theory is based essentially in two theorems, we shall present them at any order and for arbitrary dimension.
We shall apply this theory to the study of the periodic solutions of the van der Pol differential equation, Lienard differential systems, the Rossler differential system, and to some Hamiltonian systems.
Registration includes: attendance to the lectures, documentation package, copy of the course notes, lunch tickets, social dinner, and coffee breaks.

Early bird registration fee: 300 €
Registration fee: 348€​

Early bird Registration: before November 20, 2013
Deadline for registration and payment: January 18, 2014 (extended)

IMPORTANT: To register click on one of the Register buttons at the beginning or at the end of the page. ​ 

Grants information
If you wish to apply for a grant, please fill out the registration form of the RTNS2014

A group reservation has been made in Hotel Campus, in the UAB campus, where the CRM is located. For further information click here​

For other lodging suggestions in the area please click here​

For off-campus accommodation click here​

Further information

Please check the following link:​

Contact information
If you have any questions please contact:
Neus Portet (