Long term numerical integrations of the orbits of the outer planets within the LONGSTOP research project, combined with an adequate processing and filtering of the output, have allowed to recover 30 far unknown variations in the major semiaxes of the planets with period of about 1 million years. An attempt at computing the same variations analytically.has shown that small divisors in mean motion can significantly increase the amplitude of a secular effect. The secular frequency of these energy variations involves the pericentres of Jupiter and Uranus and turns out to play a major role in shaping the dynamical structure of the outer solar system. It appears also in a secular small divisor' of much a longer period (about 31 million years) recovered from the output of the 100
million years integration LONGSTOP IB. This very small divisor seems to be responsible for the accumulation of spectral lines in some regions of the long-period spectum of the outer solar system. The accumulation of spectral lines is known to be related to the presence of non regular regions of motion in the phase space. These findings have stimulated us to revisit the old problem
of regular and non-regular motion of planetary orbits from the viewpoint of both the convergence of the series of classical secular perturbation theories and the modem concept of predictability
horizon for non-integrable dynamical systems.
Cliromospheric activity is found in ten types of stars, both single and binary. Variability at many time scales is reviewed, from minutes to centuries. The emphasis is on what is not understood, incorrecty understood, and understood but not appreciated. Observational results in hand include photometry, spectroscopy, spectrophotometry, speckle interferometry, magnetic flelds, and orbltal period variations. Certain physical mechanisms responsible for variability are discussed, making the distinction between the well-established, tlie suspected, and the posslble. Specific topics
include flares, rotation, differential rotation, synchronization, circularization, starspots, spot models, migratlon periods, spot cycles, magnetic activity cycles, sector structure, Maunder minima,
pulsation, light curve solutions, convective envelope changes, mass transfer, mass loss, and orbital period variations. Specific directions for future research are identified.