The tent map is an elementary example of an interval map possessing many
interesting properties, such as dense periodicity, exactness, Lipschitzness and
a kind of length-expansiveness. It is often used in constructions of dynamical
systems on the interval/trees/graphs. The purpose of the present paper is to
construct, on totally regular continua (i.e. on topologically rectifiable
curves), maps sharing some typical properties with the tent map. These maps
will be called length-expanding Lipschitz maps, briefly LEL maps. We show that
every totally regular continuum endowed with a suitable metric admits a LEL
map. As an application we obtain that every totally regular continuum admits an
exactly Devaney chaotic map with finite entropy and the specification property.Comment: 27 pages. arXiv admin note: substantial text overlap with
arXiv:1112.601