Continuity of Lyapunov Exponents and Cantor spectrum for a class of C2 Quasiperiodic Schr\"odinger Cocycles
Duration: 47 mins 9 secs
Share this media item:
Embed this media item:
Embed this media item:
About this item
| Description: |
Wang, Y (Nanjing University)
Wednesday 08 April 2015, 15:00-16:00 |
|---|
| Created: | 2015-04-13 10:19 |
|---|---|
| Collection: | Periodic and Ergodic Spectral Problems |
| Publisher: | Isaac Newton Institute |
| Copyright: | Wang, Y |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-author: Zhenghe Zhang (Rice University)
We show that for a class of C2 quasiperiodic potentials and for any fixed \emph{Diophantine} frequency, the Lyapunov exponents of the corresponding Schr\"odinger cocycles are uniformly positive and weakly H\"older continuous as function of energies. Moreover, we show that the spectrum is Cantor. Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions. We also apply it to general quasiperiodic SL(2,\R) cocycles. |
|---|---|
Available Formats
| Format | Quality | Bitrate | Size | |||
|---|---|---|---|---|---|---|
| MPEG-4 Video | 640x360 | 1.94 Mbits/sec | 686.73 MB | View | Download | |
| WebM | 640x360 | 475.95 kbits/sec | 164.42 MB | View | Download | |
| iPod Video | 480x270 | 522.07 kbits/sec | 180.29 MB | View | Download | |
| MP3 | 44100 Hz | 249.75 kbits/sec | 86.34 MB | Listen | Download | |
| Auto * | (Allows browser to choose a format it supports) | |||||