2015/05/27 by Wang, Lin, Zhu, Yujun
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1505.07177
Let f be a partially hyperbolic diffeomorphism on a closed (i.e., compact and boundaryless) Riemannian manifold M with a uniformly compact center foliation Wc. The relationship among topological entropy h(f), entropy of the restriction of f on the center foliation h(f, Wc) and the growth rate of periodic center leaves pc(f) is investigated. It is first shown that if a compact locally maximal invariant center set Λ is center topologically mixing then f|Λ has the center specification property, i.e., any specification with a large spacing can be center shadowed by a periodic center leaf with a fine precision. Applying the center spectral decomposition and the center specification property, we show that h(f)≤ h(f,Wc)+pc(f). Moreover, if the center foliation Wc is of dimension one, we obtain an equality h(f)= pc(f).