is there a normal.dot equivalent

MS Word uses the “normal.dot” template as the default formatting for new documents, and this can be customized.

What is the equivalent for LibreOffice Writer?

If not the user chooses a specific template, a new document of any document class is created from the template set as the default for the class by the user if any. All the user’s templates can be created and edited by the user. If no default template is set for a class (‘Application’), a built-in one is used which cannot be edited.

Go > File > Templates > Manage Templates (Ctrl+Shift+N) to see how it works. > File > New > Template opens the same dialog.

It’s a bit different for presentations, and more different for database applications. No editable templates exist for ‘Math’ as far as I know.