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IRP Low dimensional dynamical systems and applications  Part II (ONLINE)
Sign into May 07, 2021
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Description
The main objects of interest in any dynamical system depending on parameters, no matter in which specific framework occurs, are the following:

The phase portrait for a fixed parameter of the system, which serves to determine the future value of the system features (or system states) in the phase space based on their present values;

The bifurcation diagram in the parameter space, which is meant to describe how a specific feature of the system varies as we move the parameters. In this respect it deserves particular attention the bifurcation phenomena that occur at those parameters which lie on the boundary between qualitatively different phase portraits.
Understanding these objects is formalized into different statements or challenges depending on the context. In particular there is a preliminary division based on whether the evolution of the process is continuous (real time) or discrete (natural or integer time), but there are other relevant considerations as the dimension of the problem (i.e., number of features we wish to observe), the topology of the phase space, the type of bifurcations in the parameter space, etc. The origin of the discrete version goes back to the studies of the chaotic dynamics by A.N. Sharkovskii (1964) and T.Y. Li and J.A. Yorke (1975) for the real case, together with the works of Cayley about Newton’s method (1879), the memoirs of P. Fatou and G. Julia (1920), and the notes of Orsay written by A. Douady and J.H. Hubbard (1982). Both scenarios real and complex show that very simple models in low dimension can exhibit extremely rich dynamics. In this context the present proposal focuses in problems related to topological and combinatorial dynamics and the description of the period set of continuous maps in graphs and trees. We also want to study the topological and analytical properties of the connected components of the Fatou set and the dynamics on their boundaries, the existence and distribution of wandering domains inside the Fatou set and the description of the parameter space and its bifurcations.
Scientific Committee
Núria Fagella  Universitat de Barcelona 
Francesc Mañosas  Universitat Autònoma de Barcelona 
Michal Misiurewiz  Indiana University – Purdue University Indianapolis 
Robert Roussarie  Université de Bourgogne 
Gwyneth Stallard  Open University 
Organizers
Peter De Maesschalck  University of Hasselt 
Antonio Garijo  Universitat Rovira i Virgili 
Xavier Jarque  Universitat de Barcelona 
David Juher  Universitat de Girona 
Boguslawa Karpinska  Technical University of Warsaw 
Lubomir Snoha  University of Bratislava 
Joan Torregrosa  Universitat Autònoma de Barcelona 
Jordi Villadelprat  Universitat Rovira i Virgili 
Invited Visitng Researchers
Click to open list
Jozef  Bobok  Czech Technical University in Prague 
Henk  Bruin  University of Vienna 
Claudio  Buzzi  Universidade Estadual Paulista 
Peter  De Maesschalck  Universiteit Hasselt 
Kealey  Dias  City University of New York 
Igsyl  Domínguez  Pontificia Universidad Católica de Chile 
Vasiliki  Evdoridou  The Open University 
Nuria  Fagella  Universitat de Barcelona 
Xavier  Jarque  Universitat de Barcelona 
Dominik  Kwietniak  Jagiellonian University in Kraków 
Kirill  Lazebnik  Caltech University 
Jérôme  Los  Université d’AixMarseille 
Michal  Misiurewicz  Indiana University 
Piotr  Oprocha  AGH University of Science and Technology 
Daniel  Panazzolo  Université de HauteAlsace 
Salomón  Rebollo Perdomo  Universidad del BíoBío 
Miriam  Romero  Universidad Autónoma del Estado de Morelos 
Robert  Roussarie  Université de Bourgogne 
Mitsuhiro  Shishikura  Kyoto University 
Lubomír  Snoha  Matej Bel University 
Bishnu Hari  Subedi  Tribhuvan University 
Jordi  Villadelprat  Universitat Rovira i Virgili 
Acknowledgements
For inquiries about the activity please contact the research programs coordinator Ms. Núria Hernández at nhernandez@crm.cat
