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Detecting resonances in conservative maps using evolutionary algorithms. (English) Zbl 1227.37008

Summary: A numerical method is proposed for detecting resonances of conservative maps which reduces this task to an optimization problem. We then solve this problem using evolutionary algorithms, which are methods for global optimization inspired by biological evolution. The proposed methodology is simple and can be easily applied to maps of arbitrary dimensions. In this letter we apply it to several examples of 2- and 4-dimensional conservative maps, with quite promising results concerning integrability, the location of resonances and the presence of chaotic regions surrounding the island chains that correspond to these resonances.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
35B34 Resonance in context of PDEs
35B06 Symmetries, invariants, etc. in context of PDEs
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37M05 Simulation of dynamical systems
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