| Title | APPROXIMATION PROPERTIES ON INVARIANT MEASURE AND OSELEDEC SPLITTING IN NON-UNIFORMLY HYPERBOLIC SYSTEMS |
| Authors | Liang, Chao Liu, Geng Sun, Wenxiang |
| Affiliation | Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China. Cent Univ Finance & Econ, Dept Appl Math, Beijing 100081, Peoples R China. Cent Univ Finance & Econ, China Inst Adv Study, Beijing 100081, Peoples R China. |
| Keywords | Independence number invariant measure mean angle DIFFERENTIAL-SYSTEMS DYNAMICAL-SYSTEMS PROBABILITY EXPONENTS |
| Issue Date | 2009 |
| Publisher | transactions of the american mathematical society |
| Citation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY.2009,361,(3),1543-1579. |
| Abstract | We prove that each invariant measure in a non-uniformly hyperbolic system can be approximated by atomic measures on hyperbolic periodic orbits. This contributes to our main result that the mean angle ( Definition 1.10), independence number ( Definition 1.6) and Oseledec splitting for an ergodic hyperbolic measure with simple spectrum can be approximated by those for atomic measures on hyperbolic periodic orbits, respectively. Combining this result with the approximation property of Lyapunov exponents by Wang and Sun, 2005 ( Theorem 1.9), we strengthen Katok's closing lemma ( 1980) by presenting more extensive information not only about the state system but also its linearization. In the present paper, we also study an ergodic theorem and a variational principle for mean angle, independence number and Liao's style number ( Definition 1.3) which are bases for discussing the approximation properties in the main result. |
| URI | http://hdl.handle.net/20.500.11897/314727 |
| ISSN | 0002-9947 |
| Indexed | SCI(E) |
| Appears in Collections: | 数学科学学院 |
