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On quasi-weakly almost periodic points

Content Provider	Springer Nature Link
Author	He, WeiHong Yin, JianDong Zhou, ZuoLing
Copyright Year	2013
Abstract	The core problem of dynamical systems is to study the asymptotic behaviors of orbits and their topological structures. It is well known that the orbits with certain recurrence and generating ergodic (or invariant) measures are important, such orbits form a full measure set for all invariant measures of the system, its closure is called the measure center of the system. To investigate this set, Zhou introduced the notions of weakly almost periodic point and quasi-weakly almost periodic point in 1990s, and presented some open problems on complexity of discrete dynamical systems in 2004. One of the open problems is as follows: for a quasi-weakly almost periodic point but not weakly almost periodic, is there an invariant measure generated by its orbit such that the support of this measure is equal to its minimal center of attraction (a closed invariant set which attracts its orbit statistically for every point and has no proper subset with this property)? Up to now, the problem remains open. In this paper, we construct two points in the one-sided shift system of two symbols, each of them generates a sub-shift system. One gives a positive answer to the question above, the other answers in the negative. Thus we solve the open problem completely. More important, the two examples show that a proper quasi-weakly almost periodic orbit behaves very differently with weakly almost periodic orbit.
Starting Page	597
Ending Page	606
Page Count	10
File Format	PDF
ISSN	16747283
Journal	Science in China Series A: Mathematics
Volume Number	56
Issue Number	3
e-ISSN	18691862
Language	English
Publisher	SP Science China Press
Publisher Date	2013-01-18
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	weakly almost periodic point quasi-weakly almost periodic point minimal center of attraction Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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