Giorgio Turchetti
Full professor at the Department of Physics University of Bologna from 1987 to 2012. Reasearch area non linear dynamics. Main contribtion: theory of non linear betatronic motion in circular accelerators withBirkhoff normal forms.
Chapters authored
Fast Indicators for Orbital Stability: A Survey on Lyapunov and Reversibility Errors
We present a survey on the recently introduced fast indicators for Hamiltonian systems, which measure the sensitivity of orbits to small initial displacements, Lyapunov error (LE), and to a small additive noise, reversibility error (RE). The LE and RE are based on variational methods and require the computation of the tangent flow or map. The modified reversibility error method (REM) measures the effect of roundoff and is computed by iterating a symplectic map forward and backward the same number of times. The smoothest indicator is RE since it damps the oscillations of LE. It can be proven that LE and RE grow following a power law for regular orbits and an exponential law for chaotic orbits. There is a numerical evidence that the growth of RE and REM follows the same law. The application to models of celestial and beam dynamics has shown the reliability of these indicators.
Part of the book: Progress in Relativity