Given a continuous map
on a metric space, it induces the maps
, on the hyperspace of nonempty compact subspaces of
X, and
[...] Read more.
Given a continuous map
on a metric space, it induces the maps
, on the hyperspace of nonempty compact subspaces of
X, and
, on the space of normal fuzzy sets, consisting of the upper semicontinuous functions
with compact support. Each of these spaces can be endowed with a respective metric. In this work, we studied the relationships among the dynamical systems
,
, and
. In particular, we considered several dynamical properties related to chaos: Devaney chaos,
-transitivity, Li–Yorke chaos, and distributional chaos, extending some results in work by Jardón, Sánchez and Sanchis (Mathematics 2020, 8, 1862) and work by Bernardes, Peris and Rodenas (Integr. Equ. Oper. Theory 2017, 88, 451–463). Especial attention is given to the dynamics of (continuous and linear) operators on metrizable topological vector spaces (linear dynamics).
Full article