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Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics (DANCE Winter School)

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Advanced course / School
From January 27, 2014
to January 31, 2014

Presentation

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.

 Coordinators

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

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

Courses

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.
Topics:
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-bod  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.
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.
Topics:
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.
 ​

LIST OF PARTICIPANTS

Lluís Alsedà Centre de Recerca Matemàtica
Benjamin Anwasia Universidade do Minho
Montserrat Aranda Universitat Politècnica de Catalunya
John Alexander Arredondo Centro de Ciencias Matemáticas de la UNAM
Esther Barrabés Universitat de Girona
Noemi Bozek Cracow University of Technology
José Luis Bravo Universidad de Extremadura
Marta Canadell Universitat de Barcelona
Sergio Alejandro Carrillo Universidad de Valladolid
Oriol Castejón Universitat Politècnica de Catalunya
Montserrat Corbera Subirana Universitat de Vic
Paula Cordoba Universitat Politècnica de Catalunya
Josep Maria Cors Universitat Politècnica de Catalunya
Iris De Universidade Estadual de Campinas
Amadeu Delshams Universitat Politècnica de Catalunya
Roberta Fabbri Università degli Studi di Firenze
Ariadna Farrés Universitat de Barcelona
Ekaterina Felk Saratov State University
jinglang Feng Delft University of Technology
Ernest Fontich Universitat de Barcelona
Jorge Galan Universidad de Sevilla
Laura Garcia Universitat de Girona
Belén García Universidad de Oviedo
Isaac García Universitat de Lleida
Johanna Denise García Saldaña Universidad Católica de la Santísima Concepción
Anna Geyer Universitat Autònoma de Barcelona
Jose Gines Universidad de Murcia
Gerard Gomez Universitat de Barcelona
Albert Granados Technical University of Denmark
Alex Haro Universitat de Barcelona
Martin Himmel Johannes Gutenberg Universität Mainz
Jackson Itikawa Universitat Autònoma de Barcelona
Angel Jorba Universitat de Barcelona
Marc Jorba Universitat de Barcelona
Daniel Juan Universidade Federal de Santa Catarina
Piotr Kamienski Jagiellonian University in Kraków
Alexey Kazakov Udmurt State University
Karel Kenens Hasselt University
Marta Kowalczyk Nicolaus Copernicus University
Jaume Llibre Universitat Autònoma de Barcelona
Alejandro Luque Universitat de Barcelona
Jennifer Luque Universitat Politècnica de Catalunya
Ana Manzanera Universitat Politècnica de Catalunya
Ismael Maroto Universidad de Valladolid
Miguel Martínez Universitat Politècnica de Catalunya
Oscar Eduardo Martínez Universidad Sergio Arboleda
Regina Martínez Universitat Autònoma de Barcelona
Susana Maza Universitat de Lleida
Narcís Miguel Politecnico di Milano
Richard Moeckel University of Minnesota
Hani Mohammed University of Calgary
Francisco Javier Molero Universidad de Murcia
Josep-Maria Mondelo Universitat Autònoma de Barcelona
Hernán Neciosup
Carmen Núñez Universidad de Valladolid
Rafael Obaya Universidad de Valladolid
Zubin Olikara Institut d’Estudis Espacials de Catalunya
Merce Olle Universitat Politècnica de Catalunya
Fabrizio Paita Universitat Politècnica de Catalunya
Daniel Pérez Universitat de Barcelona
Jesús S. Pérez del Rio Universidad de Oviedo
Enrique Ponce Universidad de Sevilla
Maja Resman University of Zagreb
Andrés Mauricio Rivera Pontificia Universidad Javeriana
David Rojas Universitat de Girona
Pablo Roldan Universitat Politècnica de Catalunya
Abraham De la Rosa Universitat Politècnica de Catalunya
Laura Rueda Universitat Politècnica de Catalunya
Patricia Sanchez Universitat Politècnica de Catalunya
Flora Sayas Universidad Pública de Navarra
Carles Simó Universitat de Barcelona
Adrià Simon Universitat Politècnica de Catalunya
Anna Tamarit Universitat Politècnica de Catalunya
Claudia Tamayo Universitat Autònoma de Barcelona
Joan Carles Tatjer Universitat de Barcelona
Francisco Torres Universidad de Sevilla
Narani van Centre de Recerca Matemàtica
Patricia Verrier University of Strathclyde
Arturo Vieiro Universitat de Barcelona
Enrique Vigil Universidad de Oviedo
Domagoj Vlah University of Zagreb
Kesheng Wu
Jeroen Wynen Hasselt University
Mohammad Zaman University of Groningen
Xiang Zhang Shanghai Jiao Tong University
Lei Zhao University of Groningen

​​

INVOICE/PAYMENT INFORMATION

IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.

UPF | UB | UPC | UAB

*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to comptabilitat@crm.cat with your name and the institution internal reference number that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed.

Paying by credit card

IF YOU PAY VIA CREDIT CARD but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to comptabilitat@crm.cat providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).

LODGING INFORMATION

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BARCELONA AND OFF-CAMPUS 

 

For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat​​

 

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