  The solar photosphere and the outer layer of the Sun's interior are
characterized by convective motions, which display a chaotic and turbulent
character. In this work, we evaluated the pseudo-Lyapunov exponents of the
overshooting convective motions observed on the Sun's surface by using a method
employed in the literature to estimate those exponents, as well as another
technique deduced from their definition. We analyzed observations taken with
state-of-the-art instruments at ground- and space-based telescopes, and we
particularly benefited from the spectro-polarimetric data acquired with the
Interferometric Bidimensional Spectrometer, the Crisp Imaging
SpectroPolarimeter, and the Helioseismic and Magnetic Imager. Following
previous studies in the literature, we computed maps of four quantities which
were representative of the physical properties of solar plasma in each
observation, and estimated the pseudo-Lyapunov exponents from the residuals
between the values of the quantities computed at any point in the map and the
mean of values over the whole map. In contrast to previous results reported in
the literature, we found that the computed exponents hold negative values,
which are typical of a dissipative regime, for all the quantities derived from
our observations. The values of the estimated exponents increase with the
spatial resolution of the data and are almost unaffected by small
concentrations of magnetic field. Finally, we showed that similar results were
also achieved by estimating the exponents from residuals between the values at
each point in maps derived from observations taken at different times. The
latter estimation technique better accounts for the definition of these
exponents than the method employed in previous studies.
