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Kolmogorov Pathways from Integrability to Chaos and Beyond
[chapter]
2003
Lecture Notes in Physics
Two limits of Newtonian mechanics were worked out by Kolmogorov. On one side it was shown that in a generic integrable Hamiltonian system, regular quasi-periodic motion persists when a small perturbation is applied. This result, known as Kolmogorov-Arnold-Moser (KAM) theorem, gives mathematical bounds for integrability and perturbations. On the other side it was proven that almost all numbers on the interval between zero and one are uncomputable, have positive Kolmogorov complexity and,
doi:10.1007/978-3-540-39668-0_1
fatcat:4u4agw2ue5apljqry2xoh4ani4