Standard map

The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving <a href="/facts/Chaotic_map/LTC17vsF">chaotic map</a> from a square with side 
 
 
 
 2
 π
 
 
 {\displaystyle 2\pi }
 
 onto itself. It is constructed by a <a href="/facts/Poincar%C3%A9_map/pd15LII2">Poincaré's surface of section</a> of the <a href="/facts/Kicked_rotator/FvyJhNoK">kicked rotator</a>, and is defined by:

p
          
            n
            +
            1
          
        
        =
        
          p
          
            n
          
        
        +
        K
        sin
        ⁡
        (
        
          θ
          
            n
          
        
        )
      
    
    {\displaystyle p_{n+1}=p_{n}+K\sin(\theta _{n})}

θ
          
            n
            +
            1
          
        
        =
        
          θ
          
            n
          
        
        +
        
          p
          
            n
            +
            1
          
        
      
    
    {\displaystyle \theta _{n+1}=\theta _{n}+p_{n+1}}

where 
 
 
 
 
 p
 
 n
 
 
 
 
 {\displaystyle p_{n}}
 
 and 
 
 
 
 
 θ
 
 n
 
 
 
 
 {\displaystyle \theta _{n}}
 
 are taken modulo 
 
 
 
 2
 π
 
 
 {\displaystyle 2\pi }
 
.
The properties of chaos of the standard map were established by <a href="/facts/Boris_Chirikov/1DKnurlv">Boris Chirikov</a> in 1969.

Standard map open-in-new

Standard map