Stable Weakly Shadowable Volume-preserving Systems Are Volume-hyperbolic

作     者：Mrio BESSA Manseob LEE Sandra VAZ 

作者机构：Universidade da Beira Interior Rua Marquês d’vila e Bolama 6201-001 Covilh Portugal Department of Mathematics Mokwon University Daejeon 302-729 Republic of Korea 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第6期

页      面：1007-1020页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by National Funds through FCT-"Fundao para a Ciênciae a Tecnologia"(Grant No.PEst-OE/MAT/UI0212/2011) supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology,Korea(Grant No.2011-0007649) 

主　　题：Weak shadowing,dominated splitting,hyperbolicity 

摘      要：We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.