• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1115-1122
• /
• 1996

In study of the dynamics of a map f from a topological space X to itself, a central role is played by the various recursive properties of the points of X. One such property is periodicity. A weaker property is that of being nonwandering. Intermediate recursive properties include almost periodicity and recurrence.

• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.2
• /
• pp.75-80
• /
• 2024

In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.1
• /
• pp.101-107
• /
• 2000

For a continuous map f of the circle to itself, we show that if P(f) is closed, then ${\Gamma}(f)$ is closed, and ${\Omega}(f)={\Omega}(f^n)$ for all n > 0.

• 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 the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• pp.647-651
• /
• 2015

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.

• The Pure and Applied Mathematics
• /
• v.2 no.2
• /
• pp.157-162
• /
• 1995

Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)