A universal instability of many-dimensional oscillator systems

May, 1979
117 pages
Published in:
  • Phys.Rept. 52 (1979) 263-379

Citations per year

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Abstract: (Elsevier)
The purpose of this review article is to demonstrate via a few simple models the mechanism for a very general, universal instability - the Arnold diffusion—which occurs in the oscillating systems having more than two degrees of freedom. A peculiar feature of this instability results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations. The instability takes place generally for very special initial conditions (inside the so-called stochastic layers) which are, however, everywhere dense in the phase space of the systsm.
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