Uniformly Distributed Periodic Orbits of Endomorphisms on n-tori
Daohua Yu , Shaobo Gan
Frontiers of Mathematics ›› 2025, Vol. 20 ›› Issue (5) : 961 -978.
Uniformly Distributed Periodic Orbits of Endomorphisms on n-tori
We prove that any ergodic endomorphism on an n-torus admits a sequence of periodic orbits uniformly distributed in the metric sense. As a corollary, an endomorphism on the torus is ergodic if and only if the Haar measure can be approximated by periodic measures.
Ergodic / periodic orbit / uniformly distributed / Haar measure / torus / 37D30
| [1] |
|
| [2] |
|
| [3] |
|
| [4] |
|
| [5] |
|
| [6] |
|
| [7] |
Huang W., Lian Z., Ma X., Xu L., Zhang Y., Ergodic optimization for a class of typical maps. 2019, arXiv:1904.01915v3 |
| [8] |
|
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
|
Peking University
/
| 〈 |
|
〉 |