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The Eclipse Mapping Method is an indirect imaging technique that transforms the shape of the eclipse light curve into a map of the surface brightness distribution of the occulted regions. Three decades of application of this technique to the investigation of the structure, the spectrum and the time evolution of accretion discs around white dwarfs in cataclysmic variables have enriched our understanding of these accretion devices with a wealth of details such as (but not limited to) moving heating/cooling waves during outbursts in dwarf novae, tidally-induced spiral shocks of emitting gas with sub-Keplerian velocities, elliptical precessing discs associated to superhumps, and measurements of the radial run of the disc viscosity through the mapping of the disc flickering sources. This chapter reviews the principles of the method, discusses its performance, limitations, useful error propagation procedures, as well as highlights a selection of applications aimed at showing the possible scientific problems that have been and may be addresses with it.
We present the Dynamic Eclipse Mapping (DEM) method designed specifically to reconstruct the surface intensity patterns of non-radial stellar oscillations in eclipsing binaries. The method needs a geometric model of the binary, accepts the light curv
We show that discs accreting onto the magnetosphere of a rotating star can end up in a trapped state, in which the inner edge of the disc stays near the corotation radius, even at low and varying accretion rates. The accretion in these trapped states
It is quite likely that self-gravity will play an important role in the evolution of accretion discs, in particular those around young stars, and those around supermassive black holes. We summarise, here, our current understanding of the evolution of
The growth process of proto-planets can be sped-up by accreting a large number of solid, pebble-sized objects that are still present in the protoplanetary disc. It is still an open question on how efficient this process works in realistic turbulent d
Planetary rotation rates and obliquities provide information regarding the history of planet formation, but have not yet been measured for evolved extrasolar planets. Here we investigate the theoretical and observational perspective of the Rossiter-M