Hi Bert,
I am not familiar with filemaker, but Mendix does support offline mobile with data synchronization. Here is some official documentation about the abilities and limitations of Mendix when building an app with offline synchronization:
https://docs.mendix.com/refguide/offline
https://docs.mendix.com/refguide6/configuring-hybrid-mobile-apps-to-run-offline
Many things function the same online and offline, but as of today executing traditional microflows is not possible when offline. Mendix executes the business logic on the application server, so executing client side business logic requires some Javascript.
Hopefully this gets you started!