The 6th Summer School on Geometry, Mechanics and Control will be held in La Cristalera (Miraflores de la Sierra, Spain) on June 22th–26th, 2012. This School is an activity within the ICMAT  Severo Ochoa Program. 

Latest news:

  • Photos 
  • Included Iserles' slides [PDF]
  • Included the references of Montaldi's course 
  • Included the Posters
  • Problem Session (D. Holm) [PDF] with the solutions [PDF]
  • The Slides of Holm's Course [PDF]
  • The Notes of the course D. Holm [PDF]
  • The list of Posters and the schedule Poster-Communication session
  • The schedule
  • Registration: no later than May 20, 2012.
  • Accommodation: no later than May 20, 2012.

  • Scholarships: no later than May 10, 2012.
  • Abstract submission for posters: no later than May 30, 2012.


Important dates:

Registration: no later than May 20, 2012.

Accommodation: no later than May 20, 2012.

Scholarships: no later than May 10, 2012.

Abstract submission for posters: no later than May 30, 2012. Please send your abstract to


D. Holm (Imperial College, United Kingdom) — Euler-Poincaré Theory: From the Rigid Body to Solitons

                        The Notes of  Holm's Course   [PDF];

                        The Slides of Holm's Course [PDF])

                        Problem Session (D. Holm) [PDF] with the solutions [PDF]

A. Iserles (University of Cambridge, United Kingdom) —Lie-group methods for ODEs. Slides [PDF]
J. Montaldi (University of Manchester) — Dynamics in Symmetric Hamiltonian Systems
References of  Montadi's course
Part 1: Series of 4 papers by James Montaldi, Mark Roberts and Ian Stewart (the first is mostly descriptive):

Nonlinear normal modes of symmetric Hamiltonian systems
In, The physics of structure formation (ed. G. Dangelmayr and W.Güttinger), Springer, 1987.

Periodic Solutions near Equilibria of Symmetric Hamiltonian Systems.
Proc. Roy. Soc. London, 325 (1988), 237-293.

Existence of nonlinear normal modes in symmetric Hamiltonian systems
Nonlinearity 3 (1990), 695-730.

Stability of nonlinear normal modes in symmetric Hamiltonian systems
Nonlinearity 3 (1990), 731-772.

Part 2:

A. Chenciner, J. Gerver, R. Montgomery, and C. Simo.
Simple choreographic motions of N bodies: a preliminary study.
In Geometry, mechanics, and dynamics, pages 287--308. Springer,  New York, 2002.

A. Chenciner and R. Montgomery.
A remarkable periodic solution of the three-body problem in the case  of equal masses.
Ann. Math., 152, 881--901, 2000.

D. Ferrario and S. Terracini.
On the existence of collisionless equivariant minimizers for the classical n-body problem.
Inventiones Math., 155, 305--362, 2003.

C. McCord, J. Montaldi, M. Roberts, and L. Sbano.
Relative periodic orbits of symmetric Lagrangian systems.
In EQUADIFF 2003, 482--493. World Sci. Publ.,  Hackensack, NJ, 2005.

K. Steckles.
Loop spaces and choreographies in dynamical systems.
PhD thesis, University of Manchester, 2011.




























































Poster-Communication sessions

  Saturday, June 23, 2012
17:30-17:40 María  Barbero: Lagrangian submanifolds and Hamilton-Jacobi equation [PDF]
17:40-17:50 Lucía Búa: Symmetries, Newtonoids vector fields and conservation laws on the Lagrangian k-symplectic formalism [PDF]
17:50-18:00 Hector Castejón: Solution of implicit differential equations using desingularization theory [PDF]
18:00-18:10 Leonardo Colombo: On the geometry of discrete higher-order lagrangian problems [PDF]
18:10-18:20 Eduardo García: A class of transformations related to magnetic Lagrangian systems [PDF]
18:20-18:30 Elisa Guzmán: Canonical definition for the analogous  map to the "Tulczyjew diffeomorphism"  for classical field theories [PDF]
18:30-19:00 Poster Session
  Sunday, June 24, 2012
16:30-16:40 Lyudmyla Grygor'yeva: Temporal aggregation, forecasting, and path continuation in estimated parametric stochastic models [PDF]
16:40-16:50 Ignazio Lacirasella: Reduction of some non-autonomous mechanical systems defined by reductive Lie groups [PDF]
16:50-17:00 Iván  Moyano: An everyday strategy analysed via Control Theory [PDF]  
17:00-17:10 Pere Daniel Prieto-Martínez: Unified formalism for higher-order non-autonomous systems [PDF]
17:10-17:20 Miguel  Teixidó: Witt-Artin Decomposition for Lagrangian Fibrations [PDF]
17:20-17:30 Miguel Vaquero: A Hamilton-Jacobi theory for singular lagrangians in the Skinner-Rusk setting [PDF]  
17:30-18:00 Poster Session



If you wish to attend the School and/or receive further information about it, please complete the enclosed Registration Form. Please, fill in the information below, and return it by e-mail to, not later than May 20, 2012.

First Name:
Family Name:
E-mail address:
Are you an undergraduate or graduate student?

The standard registration fee for participants is 200 Euros.

The fee for students, postdocs and retired scientists is 100 Euros.

The registration fee includes: conference materials and coffee breaks. Payment should be made by bank order to the following bank account:

Bank: Cajacanarias
Account: 2065 0067 61 1400223636
IBAN: ES31 2065 0067 6114 0022 3636
Please, ask your bank to write explicitly in your transference order the name "5GMC + surname of the participant" and send confirmation (your name and transfer details) by e-mail to gmcnet [at] ull [dot] es or by fax to the number +34922318145, no later than May 15, 2012.

Financial Support:

A limited number of scholarships for PhD students, advanced undergraduate students, and post-docs, will be provided by the organizers in order to partially cover the travel and/or lodging expenses. If you want to apply for a scholarship, please send your CV (and grade certificate in case you are an undergraduate student) to, not later than May 10, 2012.


Lodging reservation:

The price of the rooms at Residencia La Cristalera is 73 euros per day and per person (full board).

The number of rooms that have been reserved by the organization is limited therefore we ask you to make the reservation as soon as possible (not later than May 20, 2012).

To make the reservation of the accommodation you can send an e-mail to gmcnet [at] ull [dot] es with the following information:

If you have a preference to share the room
Check-in date:
Check-out date:



Bader Philipp Instituto de Matemática Multidisciplinar de Valencia Spain
Barbero María Universidad Carlos III de Madrid-ICMAT Spain
Búa Devesa Lucía Universidad de Santiago de Compostela Spain
Castejon Diaz Hector  Universidad Politécnica de Cataluña  Spain 
Colombo Leonardo ICMAT Spain
De León Manuel ICMAT Spain
Díaz Viviana Alejandra Universidad Nacional del Sur Argentina
Ebrahimi-Fard Kurusch ICMAT Spain
Farré Marta Universidad Complutense de Madrid Spain
García-Toraño Eduardo Ghent University Belgium
Gheorghiu Irina-Mihaela University of Zaragoza Spain
Gracia Xavier  Universidad Politénica de Cataluña  Spain 
Grygor'yeva Lyudmyla Université de Franche-Comte France
Guzmán Elisa University of La Laguna Spain
Hall James University of California, San Diego USA
Holm Darryl Imperial College UK
Iglesias  David  University of La Laguna Spain 
Iserles Arieh University of Cambridge UK
Lacirasella Ignazio University of Bari Italy
Marrero  Juan Carlos University of La Laguna Spain
Martín de Diego David ICMAT Spain 
Martínez Eduardo University of Zaragoza Spain
Montaldi James University of Manchester UK
Moyano García Iván Universidad Complutense de Madrid Spain 
Muñoz Lecanda Miguel Universidad Politécnica de Cataluña  Spain
Najafi Alishah Hassan Instituto Superior Tecnico(IST) - Lisbon Portugal
Padrón  Edith University of La Laguna Spain
Parks Helen University of California, San Diego USA
Pietrzkowski Gabriel University of Warsaw Poland
Prieto Martínez Pere Daniel Technical University of Catalonia Spain
Rigo Silvia Università degli studi di Verona – Scienze MM. FF. NN. Italy
Rodriguez-Olmos Miguel Universidad Politécnica de Cataluña  Spain
Román Roy Narciso Universidad Politécnica de Cataluña  Spain 
Salgado Modesto Universidad de Santiago de Compostela Spian
Sanjuan Szklarz Paweł Cesar Faculty of Power and Aeronautical Engineering Poland
Scandaliato Angelo L. University of California, San Diego USA
Sosa Diana University of La Laguna Spain
Teixidó Román Miguel Universitat Politècnica de Catalunya Spain
Vaquero Miguel ICMAT Spain
Vilariño Silvia Centro Universitario de la Defensa. AGM Spain



Organizing Committee

  • María Barbero Liñán (Universidad Carlos III de Madrid and Instituto de Ciencias Matemáticas, Spain)
  • Sebastián Ferraro (Universidad Nacional del Sur, Argentina)
  • David Martín de Diego (Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Spain)
  • Edith Padrón (Universidad de La Laguna, Spain)

Scientific Committee

  • Anthony Bloch (University of Michigan, USA)
  • Jair Koiller (Fundação Getulio Vargas, Brazil)
  • Manuel de León (Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Spain)
  • Juan Carlos Marrero (Universidad de La Laguna, Spain)
  • Eduardo Martínez (Universidad de Zaragoza, Spain)
  • Miguel Muñoz Lecanda (Universidad Politécnica de Cataluña, Spain)

How to get here:

Book a seat in the summer school bus before Monday, June 18, 2012.

We are now arranging the transportation to La Cristalera in Miraflores de la Sierra. In order to facilitate how to get there, there will be a bus at C/Serrano 113 in Madrid at 7.30pm on Thursday, June 21, 2012.

C/Serrano 113 was the previous home of the Institute for Mathematical Sciences (CSIC-UAM-UC3M-UCM). To get there from Barajas airport, you only need to take the subway, Line 8. This subway line has two stops in the airport, one in Terminal 4 and the other one in Terminals 1-2-3. The price is 4.50 euros. Get off at Nuevos Ministerios and walk for 15 minutes to get to C/Serrano 113.

Here you can find a map about that walk.

Once you have already picked up your luggage at the airport, it should take you around 45 minutes to get to C/Serrano 113.

When the summer school finishes, we will have a bus on Tuesday, June 26, 2012 that will take you around 3pm from La Cristalera to C/Serrano 113 in Madrid.

If you are interested in taking this bus, please send us an e-mail to gmcnetull [dot] es to book a seat for you. In the e-mail, please specify if you plan to take this bus both days, only on June 21 or only on June 26.

If you are not able to catch this bus because of your flight schedule, please keep reading the following paragraphs.

Arrival by plane

You can take a taxi from the airport, but this is an expensive choice (at least 90 Euros, but be sure to ask for the price beforehand). You can also take a taxi from the Airport to Plaza de Castilla (around 45 Euros) and then take a bus to Miraflores.

A good choice is taking the Metro from the Airport to Plaza de Castilla, and then a bus to Miraflores. At the airport, take the Metro (underground), Line 8 (pink) to "Colombia" (3 stations). Transfer in Colombia to line 9 (purple) to "Plaza de Castilla" (3 stations). This should take about 25 minutes. In any case you can ask for a free map of the Metro when you buy a ticket.

Once you have reached Plaza de Castilla there are a lot of bus stops between the two big inclined towers. Only one (number 725) goes to Miraflores de Sierra. Look for number 725 (Madrid - Plaza de Castilla to Miraflores de la Sierra, Bustarviejo). Here you can find the current timetable for bus 725.

A taxi from Plaza de Castilla to Miraflores costs minimum 70 Euros.

The trip to Miraflores de la Sierra takes approximately 60 minutes and departure is aprox. each hour from 7.30 a.m. to 23.15 p.m. Your stop is the next after "Soto del Real". Once you get off, you still have to walk around 20 minutes up along the main road to get to La Cristalera.

A one-way ticket to Miraflores by bus number 725 costs about 5.10 Euros.

Arrival by train

Coming from the North, the train station is usually Chamartin. From Chamartin, you can take the Metro (line 10: dark blue) to Plaza de Castilla but it is only one station and it is also easy to walk from Chamartin to Plaza Castilla. If you arrive at Atocha, you can take the Metro (line 1: light blue, 13 stations) to Plaza Castilla and follow the above mentioned instructions for the bus.

Arrival by car

Take the big periferial highway M-40. If you come from the south, Portugal, or the Zaragoza Highways, take direction North (N-I). If you come from the Burgos Highway (N-I) take the direction M-607 Tres Cantos- Colmenar Viejo. Go out of the M-40 to the M-607 Highway towards Tres Cantos-Colmenar viejo. When the Highway ends (roughly 30 km) take the direction Miraflores. After 30 km you will reach the village. Once there, follow the signs towards La Cristalera, or Puerto de la Morcuera. One km outside the village you will find the entrance to the residence on your left (but watch out for it since sign is not a big one and may be missed.