• Korean Journal of Mathematics
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• v.11 no.2
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• pp.161-167
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• 2003

The purpose of this paper is to study and characterize the notions of characteristic 0 and weakly almost periodicity in flows. In particular, we give sufficient conditions for the weakly almost periodic flow to be almost periodic.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.747-754
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• 2004

In this paper we investigate the existence and uniqueness of almost periodic and pseudo almost periodic solution for nonlinear differential equation with reflection of argument. For the case of almost periodic forced term, we consider the frequency modules of the solutions.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.277-282
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• 2002

In this paper we shall discuss the relationship between almost periodic fuzzy mappings and the properties of convergence theorems, and some results of almost periodic fuzzy mappings.

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

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.123-129
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• 1998

In this paper, we study some dynamical properties of a weakly almost periodic flow. In particular we get, in a weakly almost periodic flow (X,T), the groups I and A(I) of all automorphisms of I are isomorphic, where E(X) is the enveloping semigroup of (X,T) and I is the minimal right ideal in E(X).

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.351-363
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• 2020

We introduce a new concept of Stepanov weighted pseudo almost periodic functions of class r which have been established by recently in [20]. Furthermore, we study the uniqueness and existence of Stepanov weighted pseudo almost periodic mild solutions of partial neutral functional differential equations having the Stepanov pseudo almost periodic forcing terms on finite delay.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.449-455
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• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.153-158
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• 2006

In this paper, we present an elementary proof for the existence of almost periodic solutions of linear nonhomogeneous difference systems.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.171-175
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• 2004

The purpose of this paper is to investigate some lifting properties of homomorphisms of flows. It is shown that an almost one to one extension of a minimal proximal flow is proximal. It is also shown that a distal extension of a pointwise almost periodic flow is pointwise almost periodic.