Abstract
We classify the measures on SL(k,R)/ SL(k, Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero.
| Original language | English |
|---|---|
| Title of host publication | The Collected Works of Anatole Katok |
| Subtitle of host publication | In 2 Volumes |
| Publisher | World Scientific Publishing Co. |
| Pages | 2289-2336 |
| Number of pages | 48 |
| Volume | 2 |
| ISBN (Electronic) | 9789811238079 |
| ISBN (Print) | 9789811238062 |
| State | Published - 1 Jan 2024 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- General Engineering