The foundations of chaos revisited: from Poincaré to recent advancements

DOI10.1007/978-3-319-29701-9zbMath1381.37002OpenAlexW2489374575MaRDI QIDQ261513

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Publication date: 23 March 2016

Published in: Understanding Complex Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-29701-9

zbMATH Keywords

chaosmathematical modelling

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Chaotic behavior of solutions to dynamical problems in solid mechanics (74H65) Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory (37-06) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28)

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Birkhoff averages and rotational invariant circles for area-preserving maps ⋮ On the integrability of Liénard systems with a strong saddle ⋮ Efficient and reliable algorithms for the computation of non-twist invariant circles ⋮ Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average ⋮ Torus Breakdown and Homoclinic Chaos in a Glow Discharge Tube ⋮ Poincaré's stated motivations for topology ⋮ Birkhoff averages and the breakdown of invariant tori in volume-preserving maps

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