The Topological Entropy Of A Sequence Consisting Of Confluent Maps On Regular Curves

Topological entropy is a topological conjugate invariant of dynamical systems.It is also an important concept to characterize the complexity of dynamic systems.This paper studies the topological entropy of a sequence consisting of monotone mappings on regular curves.Gerald T.Seidler has proved that every homeomorphism on a regular curve has zero topological entropy.Eli Glasner and Michael Megrelishvili further proved that actions of groups on a regular continuum are null.And Hisao Kato proved that the topological entropy of every monotone map on any regular curve is zeroIn this paper,firstly,we introduce the definition of topological entropy for any set of mapping sequences on a compact metric space,which is a generalization of topological entropy and topological sequence entropy.Secondly,we study the topological entropy of a sequence consisting of several confluent maps,which has at most k-orders(actually,monotone mappings are 1-order confluent maps),and it proves that the topological entropy of a given sequence S formed by any set of monotone mappings on the regular curve X is zero.This generalizes the results of Gerald T.Seidler,Hisao Kato and Eli Glasner and Michael Megrelishvili et al.