Periodic Points and Non-wandering Points of Continuous Dynamical Systems
نویسندگان
چکیده
منابع مشابه
On Common Fixed Points, Periodic Points, and Recurrent Points of Continuous Functions
It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. We had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [0,1] if and only if {f...
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10.2. Example We consider the abstract dynamical system given in 9.18: the shift system over S where the phase space X is the product space {1, . . . , r}, for some r ≥ 2. For any R ⊆ S, there are x and U such that R(x, U) = R: simply pick x ∈ X be such that x(s) = 1 iff s ∈ R; so x might be considered as a characteristic function of R. Put U = {z ∈ X : z(1S) = 1}, a clopen subset of X. Then fo...
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Article history: Received 11 May 2008 Revised 20 September 2008 Available online 28 November 2008 Communicated by S.-W. Zhang MSC: primary 14K12 secondary 37F10
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1998
ISSN: 0001-8708
DOI: 10.1006/aima.1997.1697