Introduction:
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The systematic analysis of dynamical systems responds to the scientific interest of a better understanding of the dynamics of concrete systems. An essential role in many areas of knowledge is played by systems with a Hamiltonian structure and/or by dissipative systems.
A typical feature of Hamiltonian systems is the co-existence of regular and chaotic regimes in the phase space. Perturbations of Keplerian systems and gravitational n-body problems are well-known examples of Hamiltonian systems which, in particular, are systematically applied to many astrodynamical problems and chemical problems (e.g. the behaviour of atomic and molecular systems can be modelled as an n-body problem). Computational techniques for the detection/computation of chaotic regimes, periodic orbits, invariant tori, invariant manifolds associated to the hyperbolic objects, ... and their dependence with respect to parameters become essential in any (reasonable) explanation of the dynamics of the system.
Dissipative systems show up different dynamical properties. Among these systems are, for example, the paradigmatic Lorenz problem obtained from a simplified climate model, the Rossler problem used in certain chemical reactions, different economic models, some models of laser with a chaotic response or the Hindmarsh-Rose model, used to study the neuronal activity. The (long-time) dynamics of such systems is determined by the presence of attractors (either periodic sinks, periodic orbits, invariant tori, strange attractors,...) that may co-exist in the phase space and evolve with respect the basic parameters.
The combined use of different computational techniques is a basic tool to understand the dynamics of (both type of) these systems. These techniques include the systematic computation of chaos indicators, Lyapunov exponents, different invariants, the detection and analysis of essential bifurcations,... which can be combined (if needed) with the implementation of computer assisted proofs (interval analysis).
This special session aims to present the main advances in computational techniques for analyzing dynamical systems and to show new results, about different dynamical systems, obtained by combining several computational techniques. |
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