| Popis: |
We use a geometrical description of the dynamics of Hamiltonian systems to single out the sources of instability (and of Chaos, if any). We show that: A) the instability is driven by the fluctuations of some geometrical invariants, rather than by their average values; B) the most commonly used invariant has in general nothing to do with dynamic instability of realistic many degrees of freedom systems; C) in order to evaluate correctly the relevant quantities entering these geometric invariants, it is necessary the system settles down to a global vinal equilibrium, and that for this the number of degrees of freedom is crucial; D) the gravitating N-body system is peculiar for what it concerns both the dynamical properties and the possibility of a statistical description. So, all the claims that a geometric description of dynamics, in particular for the stellar dynamical problem, gives a direct estimate of some relaxation time are unjustified. Nevertheless, we point out that the geometrical transcription of hamiltonian systems, if carefully employed, can give deep informations about the degree of stochasticity in the dynamics, and very interesting insights on its sources. To overcome some of the limitations of the approach, for systems with few degrees of freedom and/or with time-dependent lagrangians, we introduce an extension, discussed in detail in the companion contribution[3]. |
