The dynamics of monotone maps of dendrites

Equicontinuity of maps on a dendrite with finite branch points

“…In recent years, some properties on discrete dynamical systems on dendrites, such as the topological structure of minimal sets, the depth of the center, the topological entropies of dendrite maps, are deeply discussed by many authors (see [1,2,9,10,17,18,22,24]). The interest in these subjects is motivated in part by the fact that dendrites appear as Julia sets in complex dynamics (see [4,19]).…”

Structure of dendrites admitting an existence of an arc horseshoe

“…Uncountability of the dendrite X endpoint set is characterized by existence of some subcontinuum homeomorphic to the dendrite G whose endpoint set E(G) is a Cantor set on the interval [0, 1] and each branching point is of order 3 (for the point order definition see Section 2; the dendrite G construction is given, for example in [5]). We have Lemma 1 ([6]).…”

$\overline{R} = \overline{P}$ FOR MAPS OF DENDRITES X WITH Card(End(X)) < c

“…The subjects such as the topological structure of minimal sets, the depth of the center, the topological entropy, the "forcing" relation on patterns of invariant subsets and the kneading sequence theory of dendrite maps are deeply discussed (see e.g. [Acosta & Eslami, 2007;Baldwin, 1995Baldwin, , 2007Balibrea et al, 2003;Efremova & Makhrova, 2001Kato, 1995]). The interest in these subjects is motivated in part by the fact that dendrites appear as Julia sets in complex dynamics (see [Beardon, 1991] or [Peitgen & Richter, 1986]).…”