Gauss maps for simultaneous approximation
Duration: 55 mins 18 secs
Share this media item:
Embed this media item:
Embed this media item:
About this item
| Description: |
Cheung, Y (San Francisco State University)
Thursday 03 July 2014, 10:00-10:50 |
|---|
| Created: | 2014-07-11 18:41 |
|---|---|
| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Cheung, Y |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| 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 π2/12ln2. 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. |
|---|---|
Available Formats
| Format | Quality | Bitrate | Size | |||
|---|---|---|---|---|---|---|
| MPEG-4 Video | 640x360 | 1.94 Mbits/sec | 805.49 MB | View | Download | |
| WebM | 640x360 | 1.13 Mbits/sec | 472.21 MB | View | Download | |
| iPod Video | 480x270 | 522.1 kbits/sec | 211.47 MB | View | Download | |
| MP3 | 44100 Hz | 249.74 kbits/sec | 101.28 MB | Listen | Download | |
| Auto * | (Allows browser to choose a format it supports) | |||||