page_title: Interval exchange transformation
hierarchical_section_title: Interval exchange transformation
context_page_description: In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals.
context_section_description: In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals.
caption: Graph of interval exchange transformation (in black) with 
    
      
        
          λ
          =
          (
          1
          
            /
          
          15
          ,
          2
          
            /
          
          15
          ,
          3
          
            /
          
          15
          ,
          4
          
            /
          
          15
          ,
          5
          
            /
          
          15
          )
        
      
      {\displaystyle \lambda =(1/15,2/15,3/15,4/15,5/15)}
    
   and 
    
      
        
          π
          =
          (
          3
          ,
          5
          ,
          2
          ,
          4
          ,
          1
          )
        
      
      {\displaystyle \pi =(3,5,2,4,1)}
    
  . In blue, the orbit generated starting from 
    
      
        
          1
          
            /
          
          2
        
      
      {\displaystyle 1/2}
    
  .