2017/03/17 by Kato, Hisao
#37B40 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37B45 #Secondary 54F15
paper · doi:10.48550/arxiv.1703.05888
In this paper, we define a new notion of "freely tracing property by free chains" on G-like continua and we prove that a positive topological entropy homeomorphism on a G-like continuum admits a Cantor set Z such that every tuple of finite points in Z is an IE-tuple of f and Z has the freely tracing property by free chains. Also, by use of this notion, we prove the following theorem: If G is any graph and a homeomorphism f on a G-like continuum X has positive topological entropy, then there is a Cantor set Z which is related to both the chaotic behaviors of Kerr and Li [18] in dynamical systems and composants of indecomposable continua in topology. Our main result is Theorem 3.3 whose proof is also a new proof of [6]. Also, we study dynamical properties of continuum-wise expansive homeomorphisms. In this case, we obtain more precise results concerning continuum-wise stable sets of chaotic continua and IE-tuples.