My understanding is that the bulk of an axon is myelinated, greatly adding to the efficiency of transmitting action potentials. However, the axon terminals are not myelinated. I'm wondering if the energy of an action potential is divided among the various branched terminals of an axon and, if so, how it's divided. For the purpose of this question, I think it's safe to assume that an action potential loses no energy while travelling down the main myelinated part of an axon.
From my understanding, no, this is not the case:
action potentials, in the axon terminal(s) and other non-myelinated areas, travel like a wave, thus activating all terminals with the same starting energy.
You may be interested in the Wikipedia article on
Neurotransmission. Unfortunately, a few of the citation links on that page are dead, but it should offer some good material anyway.