### Gauss maps for simultaneous approximation

Cheung, Y *(San Francisco State University)*

Thursday 03 July 2014, 10:00-10:50

Seminar Room 1, Newton Institute

#### Abstract

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.

#### Video

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