It is possible to map an ip dynamically or static on an serial interface. With inverse arp the dynamic address resolution is done by the router, trying to find out it’s mapping to the remote device and to make an entry in the local adress table. In this adress table all static and dynamic mappings are recorded.
Another definition is:
The information that correlates to the next-hop router’s Layer 3 address, and the Layer 2 address used to reach it, is called mapping. Mapping is needed on multiaccess networks.
show frame-relay map
inverse arp on the physical interface is enabled by default for configured network protocols (IP, IPX, Appletalk) on cisco routers.
Inverse ARP dynamically creates a mapping between the Layer 3 address (for example, the IP address) and the Layer 2 address (the DLCI). The end result of Inverse ARP is the same as IP ARP on a LAN: The router builds a mapping between a neighboring Layer 3 address and the corresponding Layer 2 address.
Note, „ip routing“ must be enabled on a router for frame-relay inverse-arp to work.