According to the recurrent frequency, many levels of points are found such as periodic points, almost weakly quasi-weakly and Banach points. In this paper, we consider symbolic dynamics show existence six refined between recurrence general recurrence. Despite fact that these all null-measure under any invariant measure, further they carry strong topological complexity. Each level is dense in wh...

— We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a suitable version of Hofbauer’s Markov diagram, (ii) the shadowing property and the implied entropy bound and weak rank one property, (iii) strongly positively recurrent countable state Markov shifts. Proofs are...

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem...

Firstly, it is introduced that the concepts of G-almost periodic point and G-sequence shadowing property. Then, we discuss dynamical relationship between sequence map {gk}∞k=1 limit g under G-strongly uniform convergence topological group action. We can get (1) Let be converge to where equicontinuous {yk}∞k=1 {gk}∞k=1. If limk → ∞ yk = y, then y an g; (2) are equicontinuous, limsup APG(gk) ⊂ AP...

This paper presents acoustic analysis for the purpose of automatic evaluation of shadowing speech. We use selfchecked scores of understanding, manual prosodic scores, and TOEIC scores as reference scores of learners’ shadowing speech, and compare these scores with automatic scores based on acoustic features that can reflect phoneme intelligibility and prosodic fluency in terms of intonation, an...