Several knots like unknot, $4_1$, $3_1$ are known to be Legendrian simple, i.e., Thurston-Bennequin number and rotation number determine Legendrian type completely.
How about the same notion for link cases of more than two components? In this cases, of course, we may consider those numbers in a component-wise manner.
Even for the most simplest link, i.e., Hopf link cases, I couldn't find a literature for Legendrian simplicity for that.
Is there a reason not to consider Legendrian simple links?