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Dynamics Associated to Connections Between Invariant objects with Applications to Neuroscience and Mechanics

Type of activity
Competitive project
Funding entity
Funding entity code
164.318,00 €
Start date
End date
Dynamical systems, Hamiltonian systems, Sistemas dinámicos, celestial mechanics, conexiones, connections, diffusion, difusión, integrabilidad, integrability, invariant manifolds, mecánica celeste, neurociencia, neuroscience, sistemas Hamiltonianos, variedades invariantes
This project belongs to the area of Dynamical Systems and Applications, and follows the research lines of projects MTM2009-06973,
MTM2012-31714,and MTM2015-65715-P, focusing on the local study and, mainly, the global study of continuous and discrete Dynamical
Systems using analytical and numerical tools.
The research team of the project is broad and interdisciplinary, combining experienced researchers with young researchers. Nevertheless,
we would like to increase the quantity of young people in the team. This strong research potential, jointly with a solid theoretical base,
makes it possible to cover a wide range of classic and new problems in Dynamical Systems.
The size of the team in previous projects and the diversification of the research topics pushed us to split and to present two different
proposals in this call. The present project (whose research team has 13 researchers) puts strong emphasis on the development of
mathematical theory while aims to boost the applications to Mechanics and, especially, to Neuroscience and Mathematical Biology. To
pursue this goal we have incorporated a junior co-PI with exceptional experience in Dynamical Systems and mathematical neuroscience.
We want to on keep our leadership in the areas of Arnold Diffusion and splitting of separatrices, as well as to advance in the study of
bifurcations, computation of invariant objects and integrability. But we also want to strengthen the applications of Dynamical Systems tools
to problems in infinite dimensional Dynamical Systems (partial differential equations) and mathematical Neuroscience, where the group
has already done important contributions.
In order to obtain numerical results, not only in some theoretical problems, like exponentially small splitting of separatrices, but also in
applications to Neuroscience, we follow a highly computational approach, only possible through parallel computation (the group owns and
maintains a HPC cluster). The group already has a widely recognized expertise and prestige in these fields, and we plan to continue
working on them in the following years.
Finally, it is important to stress that the group seeks a balance between working on topics for which it is already expert and internationally
recognized, like Arnold diffusion and splitting of separatrices, and working on new and challenging problems for the group, such as infinite
dimensional Dynamical Systems and Neuroscience.
We now list the main goals for the next 3 years. A more detailed subdivision in subprojects with more specific goals can be found in the research proposal.
A. Arnold diffusion
B. Exponentially small phenomena
C. Integrablility
D. Invariant objects and their bifurcations
E. Infinite-dimensional Dynamical Systems
F. Neuroscience and Mathematical Biology
Adm. Estat
Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020
Call year
Funcding program
Programa Estatal de Generación de Conocimiento y Fortalecimiento Científico y Tecnológico del Sistema de I+D+i
Funding subprogram
Subprograma Estatal de Generación de Conocimiento
Funding call
Proyectos de I+D de generación de conocimiento (antigues EXC)
Grant institution
Agencia Estatal De Investigacion