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Mukhin R. R. Chaos and nonintegrability in hamiltonian systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 1, pp. 3-24. DOI: 10.18500/0869-6632-2006-14-1-3-24

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Chaos and nonintegrability in hamiltonian systems

Mukhin Ravil Rafkatovich, Stary Oskol technological Institute. A. A. Ugarov (branch) of Federal state educational institution of higher professional education "national research technological University "MISIS" (STI nust Misa)

The article is devoted to historical development of one key aspect of Hamiltonian systems – nonintegrability, and its relation with chaotic behavior of the system. Evolution from the concept of quite integrable system to partly integrable one is shown. The relation of nonintegrability with such fundamental concepts as Kolmogorov stability, systems with divided phase space, Arnold diffusion, Zaslavsky web and others is discussed. 

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