Counterexamples of continuous maps on dendrites

We take a list of properties of continuous maps on compact metric spaces, e.g. the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, the existence of an omega-limit set containing two minimal sets and others. Our aim is to find the relations between the properties in the case of dendrite maps. To achieve the aim at least partially, we consider several examples of dendrite maps and check which of the properties particular examples have. It also helps us to understand the dynamics of dendrite maps.