  We use the theory of $x-y$ duality to propose a new definition / construction
for the correlation differentials of topological recursion; we call it
"generalized topological recursion". This new definition coincides with the
original topological recursion of Chekhov-Eynard-Orantin in the regular case
and allows, in particular, to get meaningful answers in a variety of irregular
and degenerate situations.
