2025/03/12 by Katić, Jelena, Milinković, Darko
#37B25 (Secondary) #37B35 (Primary) 54F16 #37B40 #37B45 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.09745
It is known that Morse-Smale diffeomorpshisms have the shadowing property; however, the question of whether C(f) also has the shadowing property when f is Morse-Smale remains open and has been resolved only in a few specific cases~\citeAB. We prove that if f:M→ M is a time-one-map of Morse gradient flow, the induced map C(f):C(M)→ C(M) on the hyperspace of subcontiuna does not have the shadowing property. Besides, we provide a simple criterion for f that implies C(f) has infinite topological entropy.