Kyushu Journal of Mathematics 63(2) 191-208 Oct 2009 [Refereed]

We show that if a continuous or -action of a compact metric space has the almost product property (which is weaker than the specification property), then, for any continuous function and any invariant measure, the to...

Proceedings of the American Mathematical Society 137(11) 3807-3814 Nov 2009 [Refereed]

We show the following two results, which are derived from the weaker forms of the specification property: Firstly, if an automorphism of a compact metric abelian group with finite topological entropy is ergodic under the Haar measure, then it sati...

Proceedings of the American Mathematical Society 138(1) 315-321 Jan 2010 [Refereed]

Let be a diffeomorphism of a closed manifold . In this paper, we introduce the notion of the -stable specification property for a closed -invariant set of , and we prove that satisfies a $C^1...

Discrete and Continuous Dynamical Systems 33(7) 2991-3009 Jul 2013 [Refereed]

Let be a -regular map of a closed manifold and be a locally maximal closed invariant set of . We show that satisfies the -stable specification property if and only if is a hyperb...

Discrete and Continuous Dynamical Systems 33(10) 4401-4410 Oct 2013 [Refereed]

We construct a non-ergodic maximal entropy measure of a diffeomorphisms with a positive entropy such that neither the entropy nor the large deviation rate of the measure is influenced by that of ergodic measures near it.