Stochastic instability of nonlinear oscillations. (English. Russian original) Zbl 1156.34335

Zaslavskiĭ, G. M.; Chirikov, B. V.

Sov. Phys. Usp. 14, No. 5, 549-568 (1972); translation from Usp. Fiz. Nauk 105, No. 1, 3-39 (1972).

Contents: 1. Introduction; 2. A One-dimensional nonlinear oscillator acted on by a periodic perturbation; 3. Fundamental concepts of ergodic theory; 4. Numerical experiments; 5. Stochastic Fermi acceleration; 6. The stochastic layer and the condition of overlapping resonances; 7. The random-phase approximation and the fundamental kinetic equation (master equation); 8. Bibliography.

MSC:

34F05	Ordinary differential equations and systems with randomness
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior