Abstract: Given a partially hyperbolic diffeomorphism, we introduce the notions of unstable metric entropy and unstable topological entropy. These notions coincide with the entropy defined by Ledrappier-Young and unstable volume growth rate considered by Hua-Saghin-Xia respectively. A variational principle can be established which states that unstable topological entropy is the supremum of unstable metric entropy taken over all invariant measures. Other properties such as upper semicontinuity of unstable entropy function will be also discussed. These results can be extended to the unstable pressure and the so-called u-equilibrium states can be investigated.
© 2015 All Rights Reserved. 粤ICP备14051456号
地址：广东省深圳市南山区学苑大道1088号 电话：+86-755-8801 0000 邮编：518055