Palma de Mallorca, 21 January 2019 - 25 January 2019



This is the 16th RTNS (Recent Trends in Nonlinear Science) meeting in Dynamical Systems of the DANCE (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad) Spanish network. To see other RTNS editions click here.

The workshop will take place at Edifici Sa Riera of the Universitat de les Illes Balears. Street: Miquel dels Sants Oliver, 2, 07013-Palma de Mallorca, Illes Balears, Spain.


A Poster session will be organized during the RTNS2019 for all participants. If you are interested please send title and abstract to the organizers before December 15, 2018.


Download the RTNS2019 poster here






Santiago Ibañez (Universidad de Oviedo)
Tere M-Seara (Universitat Politècnica de Catalunya)


Fernando Fernandez-Sánchez (Universidad de Sevilla)
Mark Levi (Penn state University) 
Merce Olle (Universitat Politècnica de Catalunya) 
Ronnie Pavlov (University of Denver)
Rafel Prohens (Universitat de Illes Balears)


Universitat de les Illes Balears:

María Jesús Álvarez
Antoni Buades
Bartomeu Coll
Joan Duran
José Luis Lisani
Onofre Martorell
Julia Navarro
Ana Belén Petro
Rafel Prohens
Catlina Sbert
Catalina Vich
Antonio E. Teruel

Universidad de Extremadura:

Amelia Álvarez
José Luis Bravo
Manuel Fernández

Scientific Sessions

 Dynamics near the libration points - Elena Fantino & Gerard Gómez

Elena Fantino (Khalifa University of Science Technology, United Arab Emirates)

Gerard Gómez (Universitat de Barcelona)

The course provides fundamentals of spacecraft trajectory design near the  libration points based on dynamical systems theory and associated numerical tools. After illustrating the characteristics of the main dynamical models, i.e., the two-body problem, the circular restricted three-body problem (including solar radiation pressure), Hill's model, the bicircular and quasi-bicircular four-body model and the full n-body Solar System model, the focus will be on the description of the dynamics in the vicinity of the libration points of the circular restricted three-body problem: equilibrium points, periodic orbits, quasi-periodic orbits, and invariant stable and unstable manifolds. The Lindstedt-Poincaré procedure to approximate periodic and quasi-periodic solutions will be illustrated in detail, also with the aid of numerical examples and exercises for the students. The last part of the course is an overview of past and future missions whose trajectories have been designed with this theory: from Earth-Moon transfers to missions to the libration points of the Sun-Earth system and the low-energy tours of the Galilean moons.

 The truly nonlinear dynamics of piece-wise linear systems: Bifurcations & Applications - Enrique Ponce

Enrique Ponce (Universidad de Sevilla, Spain)

Piece-wise smooth differential systems are needed nowadays both as accurate models of real engineering devices and as global reasonable models of different branches in bio-sciences. In most cases, (possibly discontinuous) piece-wise linear systems (PWL systems, for short) are enough to cope with all the problems of interest. We will review the existing theory of PWL systems in a low-dimensional context (2D/3D), putting the emphasis on the more relevant bifurcations and illustrating their usefulness in the analysis of realistic applications.

 Multiplicative Ergodic Theory and Applications - Anthony Quas

Anthony Quas (University of Victoria, Canada)

The well-known Birkhoff ergodic theorem concerns the behaviour of sums of a function along an orbit of a dynamical system. This idea first arose in kinetic theory, but the ideas have proved very fruitful in many parts of mathematics (geometry, information theory, probability, analytic and algebraic number theory to name a few). Multiplicative ergodic theory is concerned with multiplying matrices along the orbit of a dynamical system. One is given a (discrete) dynamical system T:X→X and a matrix-valued function A:X→Mdxd(R). Starting from an initial point, x0, one forms the orbit (xn) by xn=T(xn-1). In multiplicative ergodic theory, we study the behaviour of the matrix products A(xn-1) ··· A(x0). This leads to the critical idea of Lyapunov exponents and underlies the study of differential dynamical systems.
In this course, we will with an outline of ergodic theory, including some key examples. We will then recall the singular value decomposition from linear algebra, and will give a proof of the multiplicative ergodic theorem, with a view to operator-valued extensions. We will also address stability of the Lyapunov exponents along the way, and briefly describe applications to environmental dynamical systems.

 E. Fantino & G. Gómez
 Iván Sánchez Sánchez, Universitat Autònoma de Barcelona (Spain)
 Naeem Alkoumi, Bahrain University (Bahrain)
 Abdelqader Halman, Hebron University (Palestine)
 Georgios Patsios, Hasselt Universiteit (Belgium)
 Mauricio  Ascencio, Universidad del Bio-Bio (Chile)
 Francisco Romero Ruiz del Portal, Universidad Complutense de Madrid (Spain)
 Inad Nawajah, Hebron Univesity (Palestine)
 Salvador Borrós Cullell, Universitat Autònoma de Barcelona (Spain)
 Clara Cufí Cabré, Universitat Autònoma de Barcelona (Spain)
 Maria Elisa Anacleto Hoyos, Universidad del Bío-Bío (Chile)
 Javier Montes Maldonado, Universidad Politécnica de Madrid (Spain)
 Rishikesh Yadav, Sardar Vallabhbhai National Institute of Technology (India)
 José Luis García Riquelme, Universidad Politécnica de Madrid (Spain)
 José Luis Bravo Trinidad, Universidad de Extremadura (Spain)
 Bowen Liu, University of Augsburg (Germany)
 Santiago Ibáñez, Universidad de Oviedo (Spain)
 Chanyan Wang, Universitat Politècnica de Catalunya (Spain)
 Javi Gutiérrez, Universitat Politècnica de Catalunya (Spain)
 Jeroen Wynen, Hasselt University (Belgium)
 Chunwei Ye, Universitat Politècnica de Catalunya (Spain)
 Marta Pardo Araujo, Universitat Politècnica de Catalunya (Spain)
 Celsa Pardo Araujo, Universitat Politècnica de Catalunya (Spain)
 Iñigo Moreno, Universitat Politecnica de Catalunya (Spain)
 Marina Vilardell, Universitat Politècnica de Barcelona (Spain)
 Philipp Bader, Universitat Politècnica de Catalunya (Spain)
 Merce Ollé, Universitat Politècnica de Catalunya (Spain)
 Mar Giralt Miron, Universitat Politècnica de Catalunya (Spain)
 Teresa Silva, ISEL-IPL and CIMA (Portugal)
 Tere Martinez-Seara, Universitat Politècnica de Catalunya (Spain)
 Dr. Hardik  Patel, UKA Tarsadia University (India)
 Òscar Rodríguez del Río, Universitat Politècnica de Catalunya (Spain)
 Mihir Panchal, Sardar Vallabhbhai National Institute of Technology,Surat (India)
 Begoña Nicolás, Universitat de Barcelona (Spain)
 Gladston Duarte Ferreira, Universitat de Barcelona (Spain)
 Telmo Peixe, CEMAPRE - ISEG - ULISBOA (Portugal)
 Josep Maria Cors, Universitat Politècnica de Catalunya (Spain)
 Begoña Alarcón Cotillas, Universidade Federal Fluminense (Brazil)
 Yuliya Bakhanova, National Research Lobachevsky State University of Nizhni Novgorod (Russia)
 Marina Esteban, Universidad de Sevilla (Spain)
 Jose Manuel Montilla García, Universidad de Sevilla (Spain)
 Karel Kenens, Hasselt University (Belgium)
 Patricia Yanguas Sayas, Universidad Pública de Navarra (Spain)
 Ekaterina Shiryaeva, Lobachevsky State University (Russia)
 Ramakanta Meher, S.V Nationational Institute of Technology,Surat,India (India)
 Lucía Pérez, Universidad de Oviedo (Spain)
 Carmen Núñez, Universidad de Valladolid (Spain)
 Venktesh  , Universidade de Santiago de Compostela (Spain)
 Catalina Vich Llompart, Universitat de les Illes Balears (Spain)
 Rafel Prohens Sastre, Universitat de les Illes Balears (Spain)
 María Jesús Álvarez, Universitat de les Illes Balears (Spain)
 Esther Barrabés Vera, Universitat de Girona (Spain)
 Sylvia Novo, Universidad de Valladolid (Spain)
 Alfred Peris, Universitat Politècnica de València (Spain)
 Francisco Rodenas, Universidad Politécnica de Valencia  (Spain)
 Jordi Penalva Vadell, Universitat de les Illes Balears (Spain)
 Abdalhafez Alkhatib, Al-quds University (Palestine)
 Antonio E  Teruel Aguilar, Universitat de les Illes Balears (Spain)
 Ivan Pereira Sanchez, Universitat de les Illes Balear (Spain)
 Manuel Iñarrea Las Heras, Universidad de La Rioja (Spain)
 Fernando Fernández Sánchez, Universidad de Sevilla (Spain)
 Bartomeu Coll Vicens, Universitat de les Illes Balears (Spain)
 Onofre Martorell Nadal, Universitat de les Illes Balears (Spain)
 Yagor  Romano Carvalho, UAB/UNESP-IBILCE (Spain)
 Ana Belén Petro Balaguer, Universitat de les Illes Balears (Spain)
 Elísabet Vela Felardo, Sevilla (Spain)
 Enrique Ponce Núñez, Universidad de Sevilla (Spain)
 Elena Fantino, Khalifa University of Science Technology (United Arab Emirates)
 Anthony Quas, University of Victoria (Canada)
 Gerard Gómez Muntané, Universitat de Barcelona (Spain)
 Rafael Obaya, Valladolid (España)
 Yagor Romano Carvalho, UAB - UNESP/IBILCE (Spain)
 Rafael Obaya, Universidad de Valladolid (Valladolid)