**3. Chaos in Hamiltonian and conservative systems**

The modern classical theory of Hamiltonian systems reduces a problem of the analysis of dynamics of such system to the problem of its integralability, i.e. to a problem of construction of the canonical transformation reducing system to variables "action - angle" in which, as it is considered to be, movement occurs on a surface of *n* -dimensional torus and is periodic or quasiperiodic. Any nonintegrable nonlinear Hamiltonian system is considered as perturbation of integrable system, and the analysis of its dynamics is reduced to finding-out of a question on destruction or nondestruction some tori of nonperturbed system depending on value of perturbation.

In the present Section absolutely other bifurcation approach is considered for analysis of chaotic dynamics not only Hamiltonian, but also any conservative system of nonlinear differential equations. The method consists in consideration of approximating extended two-parametrical dissipative system of the equations, stable solutions (attractors) of which are as much as exact aproximations to solutions of original Hamiltonian (conservative) system. Attractors (stable cycles, tori and singular attractors) of extended dissipative system one can search by numerical methods with use the results of universal FSM (Feigenbaum-Sharkovskii-Magnitskii) theory, developed initially for nonlinear dissipative systems of ordinary differential equations and considered in detail in the previous Section of the chapter. It becomes clear what chaos is in Hamiltonian and simply conservative systems. And this chaos is not a result of destruction of some tori of nonperturbed system as it is considered to be in the modern literature, but, on the contrary, it is a result of bifurcation cascades of a birth of regular (cycles and tori) and singular attractors in extended dissipative system in accordance with the universal FSM theory when dissipation parameter tends to zero.
