On the disappearance of isolating integrals in dynamical systems with more than two degrees of freedom

C. Froeschl�, J. -P. Scheidecker
1973 Astrophysics and Space Science  
We continue to study the number of isolating integrals in dynamical systems with three and four degrees of freedom, using as models the measure preserving mappings T already introduced in previ ous papers (Froeschle, 1972; Froeschle and Scheidecker, 1973a) . Thus, we use here a new numerical method which enables us to take as indicator of stochasticity the variation with n of the two (respectively three) largest eigenvalues -in absolute magnitude -of the linear tangential mapping T 1 * of T".
more » ... is variation appears to be a very good tool for studying the diffusion process which occurs during the disappearance of the isolating integrals, already shown in a previous paper (Froeschle, 1971 ). In the case of systems with three degrees of freedom, we define and give an estimation of the diffusion time, and show that the gambler's ruin model is an approximation of this diffusion process.
doi:10.1007/bf00649179 fatcat:sktthwcriffknc4pphjrfir2om