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删除87字节 、 2021年1月3日 (日) 23:24
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:<math>f: X \to X,</math>
 
:<math>f: X \to X,</math>
  −
f:X→X,
      
a point ''x'' in ''X'' is called periodic point if there exists an ''n'' so that
 
a point ''x'' in ''X'' is called periodic point if there exists an ''n'' so that
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:<math>\ f_n(x) = x</math>
 
:<math>\ f_n(x) = x</math>
  −
f_n(x) = x
      
where <math>f_n</math> is the ''n''th [[iterated function|iterate]] of ''f''. The smallest positive [[integer]] ''n'' satisfying the above is called the ''prime period'' or ''least period'' of the point ''x''. If every point in ''X'' is a periodic point with the same period ''n'', then ''f'' is called ''periodic'' with period ''n'' (this is not to be confused with the notion of a [[periodic function]]).
 
where <math>f_n</math> is the ''n''th [[iterated function|iterate]] of ''f''. The smallest positive [[integer]] ''n'' satisfying the above is called the ''prime period'' or ''least period'' of the point ''x''. If every point in ''X'' is a periodic point with the same period ''n'', then ''f'' is called ''periodic'' with period ''n'' (this is not to be confused with the notion of a [[periodic function]]).
第32行: 第28行:     
If there exist distinct ''n'' and ''m'' such that
 
If there exist distinct ''n'' and ''m'' such that
  −
If there exist distinct n and m such that
      
如果存在不同的n和m使
 
如果存在不同的n和m使
    
:<math>f_n(x) = f_m(x)</math>
 
:<math>f_n(x) = f_m(x)</math>
  −
f_n(x) = f_m(x)
      
then ''x'' is called a '''preperiodic point'''. All periodic points are preperiodic.
 
then ''x'' is called a '''preperiodic point'''. All periodic points are preperiodic.
第148行: 第140行:     
* [[Limit cycle]]
 
* [[Limit cycle]]
 +
 +
* [[限制周期]]
    
* [[Limit set]]
 
* [[Limit set]]
 +
 +
* [[限量套]]
    
* [[Stable manifold|Stable set]]
 
* [[Stable manifold|Stable set]]
 +
 +
* [[稳定歧管|稳定集]]
    
* [[Sharkovsky's theorem]]
 
* [[Sharkovsky's theorem]]
 +
 +
* [[Sharkovsky定理]]
    
* [[Stationary point]]
 
* [[Stationary point]]
 +
 +
* [[固定点]]
    
* [[Periodic points of complex quadratic mappings]]
 
* [[Periodic points of complex quadratic mappings]]
  −
* [[限制周期]]
  −
  −
* [[限量套]]
  −
  −
* [[稳定歧管|稳定集]]
  −
  −
* [[Sharkovsky定理]]
  −
  −
* [[固定点]]
      
* [[复杂二次映射的周期点]]
 
* [[复杂二次映射的周期点]]
      
{{PlanetMath attribution|id=4516|title=hyperbolic fixed point}}
 
{{PlanetMath attribution|id=4516|title=hyperbolic fixed point}}
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