Many of the halakhot of hadasim – the myrtle branches, referred to as anaf etz avot in Vayikra 23:40 – parallel those of the lulav. They cannot be stolen or dried up, etc.
The Gemara derives the identification of the hadas as a myrtle based on its interpretation of the aforementioned passage in Vayikra, reading it to mean that the leaves must cover the branches. In so doing, the Gemara rejects a number of other possible identifications, like olive branches, dulva and hirduf.
The dulva – platanus orientalis – is a tall, non-fruit-bearing tree (it grows to 50 meters high) of the Platanaceae family that is usually grown as an ornamental tree. It is rejected in this case because its leaves do not totally cover its branches.
The hirduf – nerium oleander – is an evergreen shrub that grows to a height of four meters. Its yellowish-greenish leaves are thick and leathery with pink flowers.
Although it certainly meets the requirement to have leaves that cover the branches, it is rejected because of its toxicity. Both Abaye and Rava quote pesukim – Abaye from Mishlei (3:17) that the ways of the Torah are pleasant; Rava from Zekharya (8:19) that the Torah loves truth and peace – that are understood to indicate that a poisonous plant could not be the one chosen to perform a mitzva.
A Sage taught in the Tosefta: A dense-leaved branch is fit, and one that is not dense-leaved is unfit, even though it is a myrtle branch.
The Gemara asks: What are the circumstances of “dense-leaved tree”? Rav Yehuda said: And it is a configuration where three leaves emerge from each base. Rav Kahana said: Even two leaves emerging from one base and one leaf that covers the other two emerging from a lower base is called thick. Rav Aha, son of Rava, would purposely seek a myrtle branch configured with two leaves emerging from one base and one emerging from a lower base, since this statement emerged from the mouth of Rav Kahana. Mar bar Ameimar said to Rav Ashi: My father called a myrtle branch with that configuration a wild myrtle branch.
While the Rema permits the use of a hadas where there are two leaves on each level (Shulhan Arukh Orah Hayyim 446:3), the majority of the poskim reject that position and rule that three leaves need to be growing on each level.