Letter of Ruelle to Bowen

This letter (*) from David Ruelle to Rufus Bowen arrived just 3 months before the untimely death of Bowen. It is historically interesting not only because it is a correspondence of two important pioneers in dynamical systems theory. It is also a testimony on how scientific correspondence used to take place. With paper and pen! Here is the transcript: (*) The letter had been stuck in a book of Bowen which was given away at the Harvard library. Also historically interesting maybe in the future from the technology side. The transcript had been produced by chat GPT. I did not have to change anything except the subscripts in the formula. This is amazing because it is a rather unique hand writing. For me this is magic because I had myself (essentially the summer of 2000) worked on an OCR implementation from scratch, written in C. While it worked, it did not work well, I just appreciate the difficulty if one wanted to do that in a naive way by isolating letters. 

April 22, 1978

Dear Rufus,

The present letter is unrelated to the one I sent you two days ago,
and is motivated by "A model for Couette flow data:
which you published in the "Berkeley Turbulence Seminar."
There is a possible objection to your interpretation of the data
which goes as follows. Due to the rotational symmetry of the system,
a generic possibility is that the time periodicity corresponding to the
frequency; is one purely to the rotation of a configuration
of the fluid which is steady in a suitable rotating frame. This is
intuitive once you think of it, it can also be proved [Cf. my paper in
Arch. Rat. Mech. Anal. 51, 136-152 (1973)].

If another frequency w1 or w2 corresponds to
"intrinsic" motion of the fluid, like pulsation, which cannot
be ruled out even by going to a rotating reference frame, there is no
reason to expect that w2 or w3 will "lock in" with 
w1. This is because w1 can be changed
in an arbitrary manner by going to a suitable rotating reference frame,
and that is not true of w1 or w2

To summarize: Depending on the geometry of the system, one expects that
locking-in of frequencies will take place or not. I understand that
Fenstermacher, Golub, and Swinney are making a new experiment with two
laser beams which should throw some light on the geometry of the system.

Best regards, David.

Copy: H. Swinney J. Golub

Let me know if you need further assistance or clarification with this
letter.


Click on one of the thumbnails to see the scanned page larger:
Oliver Knill Last edit: September 9, 2024,