Chaoticity Of The Set-valued Mapping Induced By Uniform Limit Maps

Let （X,d）be a compact metric space and let f_n: Xâ†'Xbe a sequence ofcontinuous maps such that{f_n}_n=1^∞converges uniformly to a continuous andsurjective map f_n: Xâ†'X. Iff_nnis topological transitivity in stronglysuccessive way, on the one hand, we investigate the elements of_ntopologicalmixing and the chaotic behavior possessed byfnthat can be inherited by f_n. Onthe other hand, we give sufficient conditions for the chaoticity of_nthe set-valuedmapping induced by uniform limit maps.