Almost periodic points and minimal sets in topological spaces

Fujita, Chikara; Kato, Hisao

doi:10.4995/agt.2009.1737

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

2014

Publication Types

Select...

Article3

Other1

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the main problems in dynamical systems is the description of the orbit structure of a system from a topological point of view [1,3,4]. Recurrence behavior is one of the most important concepts in topological dynamics.…”

Section: Introductionmentioning

confidence: 99%

On the topology of the chain recurrent set of a dynamical system

Ahmadi

2014

Appl.Gen.Topol.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

On the topology of the chain recurrent set of a dynamical system

Ahmadi

2014

Appl.Gen.Topol.

View full text Add to dashboard Cite

show abstract

Minimal sets in compact connected subspaces

Mai

2011

Topology and its Applications

View full text Add to dashboard Cite

Recurrence, pointwise almost periodicity and orbit closure relation for flows and foliations

Yokoyama¹

2013

Topology and its Applications

View full text Add to dashboard Cite

In this paper, we obtain a characterization of the recurrence of a continuous vector field w of a closed connected surface M as follows. The following are equivalent: 1) w is pointwise recurrent. 2) w is pointwise almost periodic. 3) w is minimal or pointwise periodic. Moreover, if w is regular, then the following are equivalent: 1) w is pointwise recurrent. 2) w is minimal} is the orbit closure relation). On the other hand, we show that the following are equivalent for a codimension one foliation F on a compact connected manifold: 1) F is pointwise almost periodic. 2) F is minimal or compact. 3) F is R-closed. Also we show that if a foliated space on a compact metrizable space is either minimal or both compact and without infinite holonomy, then it is R-closed.

show abstract

Almost periodic points and minimal sets in topological spaces

Abstract: Let Γ be a group with subgroup Λ. We show, under certain conditions , that an almost periodic point for the action of Λ is also almost periodic for Γ. This is applied to obtain a theorem of Glasner.

Cited by 4 publications

References 3 publications

On the topology of the chain recurrent set of a dynamical system

On the topology of the chain recurrent set of a dynamical system

Minimal sets in compact connected subspaces

Recurrence, pointwise almost periodicity and orbit closure relation for flows and foliations

Contact Info

Product

Resources

About