EDPM, or ethylene propylene diene monomer (M-class)
synthetic rubber is the usual 'rubber' roof used on RVs and stationary buildings. It periodically needs attention as it is often covered by a sealant to block UV rays. On a stationary building, it's often covered with hot asphalt and gravel, but that doesn't work well, (especially for vehicles behind you) on an RV.
In addition, caulking at joints and objects coming through the roof should be checked every six months to be sure it's still intact. Dicor self-leveling caulk is an excellent product for caulk, also Dicor
makes liquid sealant for the periodic re-coating of the EDPM membrane.
Maintaining the roof and inspecting or repairing caulk is far cheaper than the damage done by leaks or replacing the EDPM membrane. There are alternative roof types, some are plastic 'bed-liner' like coverings, but they do cost money.