• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.39-52
• /
• 2019

The aim of this paper is to introduce the notions of (quasi) weakly almost periodic point, measure center and minimal center of attraction of amenable group actions, explore the connections of levels of the orbit's topological structure of (quasi) weakly almost periodic points and study chaotic dynamics of transitive systems with full measure centers. Actually, we showed that weakly almost periodic points and quasiweakly almost periodic points have distinct orbit's topological structure and proved that there exists at least countable Li-Yorke pairs if the system contains a proper (quasi) weakly almost periodic point and that a transitive but not minimal system with a full measure center is strongly ergodically chaotic.

• Journal of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1229-1254
• /
• 2022

In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for ℤ^d₊-actions, explore the connections of levels of the topological structure the orbits of (quasi-)weakly almost periodic points and discuss the relations between (quasi-)weakly almost periodic point and minimal center of attraction. Especially, we investigate the chaotic dynamics near or inside the minimal center of attraction of a point in the cases of S-generic setting and non S-generic setting, respectively. Actually, we show that weakly almost periodic points and quasi-weakly almost periodic points have distinct topological structures of the orbits and we prove that if the minimal center of attraction of a point is non S-generic, then there exist certain Li-Yorke chaotic properties inside the involved minimal center of attraction and sensitivity near the involved minimal center of attraction; if the minimal center of attraction of a point is S-generic, then there exist stronger Li-Yorke chaotic (Auslander-Yorke chaotic) dynamics and sensitivity (ℵ₀-sensitivity) in the involved minimal center of attraction.

• Korean Journal of Mathematics
• /
• v.8 no.1
• /
• pp.27-32
• /
• 2000

In this paper, we show that for any continuous map $f$ of the circle $S^1$ to itself, (1) $x{\in}{\Omega}(f){\backslash}\overline{R(f)}$, then $x$ is not a turning point of $f$ and (2) if $P(f)$ is non-empty, then $R(f)$ is closed if and only if $AP(f)$ is closed.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.863-868
• /
• 2011

The purpose of this paper is to study the orbit behaviours near almost periodic points. We introduce notions of uniformly recurrent and u-recurrent points and investigate some relationships between these properties.

• Communications of the Korean Mathematical Society
• /
• v.15 no.3
• /
• pp.549-553
• /
• 2000

For a continuous map of the circle to itself, we give necessary and sufficient conditions for the $\omega$-limit set of each nonwandering point to be minimal.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.277-288
• /
• 2004

In this paper, we discuss a continuous self-map of an interval and the existence of an uncountable strongly chaotic set. It is proved that if a continuous self-map of an interval has positive topological entropy, then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.247-262
• /
• 2024

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space X, a syndetically transitive semiflow (T, X, 𝜋) having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a T₃ space X, a transitive, nonminimal semiflow (T, X, 𝜋) having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.

• The Journal of the Society of Korean Medicine Diagnostics
• /
• v.9 no.1
• /
• pp.59-68
• /
• 2005

Background and purpose: Cardiovascular disease will undoubtedly rise along with the aging of the 'baby-boom' generation. The purpose of this study is to find the new index of the cardiovascular aging. Methods: The effects of aging on the heart and the arterial system are surveyed in the point of structure and function. Results: Arterial stiffening is due to the fatiguing effects of periodic stress on the arterial wall and is the main reason for increasing pulse wave velocity. The systolic hypertension is caused by the early return of wave reflection. The increased after-load by the arterial change leads to the development of left ventricular hypertrophy. The reduction in left ventricular compliance cause the impairments of the diastolic function. In contrast to the lower limb, aging effect in the upper limb are almost due to the ascending aortic pressure wave and the reflected wave from the lower limb. Conclusion: We have the following points. (1) The change of physiological pulse pattern by age can be explained by the early returning of reflected wave. (2) The atrial pulse in old age are generated by the left ventricular hypertrophy.