introduction
Dynamical systems theory looks for the milestones that organize dynamics, essentially their invariant objects and their connections. In this ambitious goal, the group has a recognized track record and a leading role, addressing it through, among others, analytical, geometrical, topological, or numerical tools, which, complemented, also contribute to a deeper understanding of the dynamics of a system. The dynamics of the systems studied, which are real or complex, can be both discrete and continuous, their dimensions are low or high, depending very much on the specific applications.
In low-dimensional systems, the search for periodic orbits and their repercussions on global dynamics is of paramount importance, especially as a result of the associated symbolic, topological, and combinatorial dynamics. The computational and numerical implementation for looking the phase portraits and bifurcation diagrams is also widely used in modelization and other applications.
In high-dimensional systems, the search for invariant tori and their disposition into normally hyperbolic invariant objects is studied especially to describe the skeleton from which emanates global dynamics, such as KAM theory, Arnold diffusion, and associated exponentially small phenomena, with special attention to applications in Celestial Mechanics, Astrodynamics, Neuroscience, and Chemistry.
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