Recursive source inclusion

[LCID Fire]

Another try - maybe someone shows some mercy and answers my question

I have a directory structure:
src
|---gtk
|    |---gtkapp.c
|    |---Makefile.am
|
|---core.c
|---Makefile.am

I'd like to use automake to build this.
The Makefile.am residing in the gtk directory looks like:
bin_PROGRAMS = gtkapp
gtkapp_SOURCES = gtkapp.c

What I'd like to do is to include core.c in the gtkapp build - but NOT
by directly adding it to gtkapp_SOURCES (I can give a good explanation
why - but it would ruin the simplicity of the example).
I already know that using a variable does not work.
I thought that maybe putting
SOURCES = core.c
into the root Makefile.am could work - but it does not. There HAS to be
a way to achieve this - but the docs are very bleak on recursive issues.