一类圆映射的混沌性质

Chaotic Behavior of One Class Circle Maps

对于圆映射ｆ（θ） ＝ ｋθ，ｋ ≥２ 为自然数，０ ≤θ≤２π．利用珋θ∈［０ ，１］ 的进位制展开： 珋θ＝ θ１ｋ ＋ θ２ｋ２ ＋ …＋ θｎｋｎ ＋ … θｎ ∈｛０ ，１，…，ｋ － １｝证明了ｆ 具有混沌性质：敏感初始条件、稠密周期点和拓扑传递性．

For circle maps f(θ)=kθ,k≥2 is a natural number,0≤θ≤2π,using the base k expansion of ∈[0,1]: =θ 1k+θ 2k 2+…+θ nk n+… θ n∈｛0,1,…,k-1｝, shown the maps f have chaotic behavior:the sensitive dependence on initial conditions;periodic points are dense and topological transitivity.