The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

Skip to content



Gauss maps for simultaneous approximation

Cheung, Y (San Francisco State University)
Thursday 03 July 2014, 10:00-10:50

Seminar Room 1, Newton Institute


Levy's constant measures the exponential growth rate for the sequence of denominators of the convergents of a real number. Khintchine proved existence for almost every real number and Levy computed the constant to be $\pi^2/12\ln2$. This result is a standard exercise in modern textbooks on ergodic theory. In this talk, we generalize it to higher dimensions with Levy's constant defined using the sequence of best approximation denominators. The main ingredient of the proof is constructing the analog of the Gauss map for continued fractions. This work is joint with Nicolas Chevallier.


The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧