KAM is like masturbation

For reasons well known in KAM theory, when solving the linear cohomological equation over a Diophantine rotation, one has to introduce an infrared cut-off \( T_{N} \), projecting on frequencies lower than \( N\), and an ultraviolet cut-off \( R_{N} \), projecting on frequencies strictly higher than \( N\).
These operators can be easily estimated in the relevant norm by applying Johnson's cut-off theorem, proved in [Co98].

Since, however, we know by construction that

\( T_{N} + R_{N} = \mathrm{Id} \)

we obtain immediately the following corollary.
Corollary 1. The visible spectrum is empty. If you publish too much in KAM, you will go blind.


Bibliographical index
[Co98]: The Big Lebowski, Ethan & Joel Coen, personal communication.