Abstract:
Let (X,f1,∞) be a nonautonomous dynamical system. We summarize known definitions
of periodic points for general nonautonomous dynamical systems and propose a new,
very natural, definition of asymptotic periodicity. Moreover, this definition is resistant to
changes of a beginning of the sequence generating the nonautonomous system. We
show the relations among these definitions and discuss their properties. We prove that
for pointwise convergent nonautonomous systems topological transitivity together with
dense set of asymptotically periodic points imply sensitivity. We also show that event for
uniformly convergent systems the nonautonomous analog of Sharkovsky's Theorem is
not valid for most definitions of periodic points.