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CRM > English > Activities > Curs 2019-2020 > IRP Low dimensional dynamical systems and applications
IRP Low dimensional dynamical systems and applications

February 3th to April 30th, 2020​ 
 
General i​nformation
 
Description
 
Dynamical systems is a wide area of research which goes beyond mathematics itself, and includes many applications. In addition, the tools are varied and come from most of the classic research lines in mathematics, such as real and complex analysis, measure theory, ergodic theory, numerical analysis and its computational implementation, topology, number theory, etc. Roughly speaking, the theory of dynamical systems consists in the rigorous study of one, several, or even infinitely many features associated to a process that depends intrinsically on parameters and that evolves when an independent variable (that we call time for obvious reasons) varies. Most of the problems in this context arise from physics (movement of celestial bodies, heat evolution in a rigid body...), biology (evolution in a structured population, neuroscience, cell growth...), economy (generational phenomena, market prices evolution...), chemistry (chemical reactions), new technologies (complex networks) or from mathematics themselves (graph theory, fractals, chaos...).

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.

​Main activities:

Advanced ​course​: Recent Trends in Nonlinear Science. February 3rd to 7th, 2020.

Conference: Bifurcations and finiteness problems in ordinary differential equations​. February 17th to 21st, 2020.



Weekly joint seminar: For the duration of the program, different dynamical systems seminars in the Barcelona area will merge into this seminar at the CRM.​

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 visiting researchers​​ (confirmed)​​
 
Krzysztof Baranski​​ ​University of Warsaw
​Anna Miriam Benini ​University of Parma
​Walter Bergweiler ​University of Kiel
​Christopher Bishop ​Stony Brook University
​Kristian Bjerklov ​KTH Royal Institute of Technology
Jozef Bobok​​ ​Czech Technical University in Prague
​Henk Bruin ​University of Vienna
Claudio Buzzi  Universidade Estadual Paulista
Colin Christopher  Plymouth University
Peter De Maesschalck  Hasselt University
​Vasiliki Evdoridou  ​Open University
Armengol Gasull  Universitat Autònoma de Barcelona
​Tobias Jäger Friedrich Schiller University Jena​
​Àngel Jorba ​Universitat de Barcelona
​Boguslawa Karpinska ​Warsaw University of Technology
​Dominik Kwietniak ​Jagiellonian University in Kraków
​Kirill Lazebnik ​CalThech University
​Jérôme Los ​Aix Marseille Université
Pavao Mardesic  Université de Bourgogne
​David Martí-Pete ​IMPAN, Warsaw
​Michal Misiurewicz ​Indiana University – Purdue University Indianapolis
​Daniel Nicks ​Nottingham University
Douglas Novaes  Universidade Estadual de Campinas
Dimitry Novikov  Weizmann institute of Science
​Piotr Oprocha ​AGH University of Science and Technology
Daniel Panazzolo  Université de Haute-Alsace
Rafel Prohens Universitat de les Illes Balears
Salomon Rebollo  Universidad del Bio Bio
​Lasse Rempe ​University of Liverpool
​Phil Rippon ​Open University
​Juan Rivera ​University of Rochester
Robert Roussarie  Université de Bourgogne
​Mitsuhiro Shishikura ​Kyoto University
​Lubomir Snoha ​Matej Bel University
​Gwyneth Stallard ​Open University
​Joan Carles Tatjer ​Universitat de Barcelona
Xiang Zhang  Shanghai Jiao Tong University
 
 Grants 
​  

The CIMPA-CRM programme aims to fund the participation of several young mathematicians from developing countries to the activities of Intensive Research Programmes at the CRM in Barcelona.

Young scientists (master students soon looking for a PhD, PhD students, postdocs) meeting those criteria and interested in the topics are much encouraged to apply for a support to participate in the Intensive Research Programme SAFAIS-2019  "Spaces of Analytic Functions: Approximation, Interpolation, Sampling".

The laureates of the CIMPA-CRM program will receive a financial support including:
  • - Roundtrip travel between your home country and Barcelona (including visa fees)
  • - Accommodation in Barcelona (in housing provided by the CRM)
  • - Per diem allowance of 600€/month, for 2 months
The candidates have to apply on the web page: http://students.cimpa.info
The applications must be submitted by September 30th, 2019.



 Further information​​
  
For inquiries about the programme please contact the research programme's coordinator Ms. Núria Hernandez at nhernandez@crm.cat​


EMS GRANT:
 
The EMS offers some travel grants to young mathematicians from less-favoured regions within the geographical area of EMS membership for presenting results at conferences or attending courses, or for research stays in foreign countries, normally up to a maximum of 900 euros in each case or 500 euros for trips within Europe.
 
Eligible researchers should use this online form​ in order to apply for travel grants.
The applications must be submitted by September 30th, 2019.​ 
 
Acknowledgements
  
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