Sinai–Ruelle–Bowen measure

<p>In the mathematical discipline of <a href="/facts/Ergodic_theory/rkqCbIy0">ergodic theory</a>, a Sinai–Ruelle–Bowen (SRB) measure is an <a href="/facts/Invariant_measure/X75B3PcM">invariant measure</a> that behaves similarly to, but is not an <a href="/facts/Ergodic/CKY3Gr9v">ergodic</a> measure. In order to be ergodic, the time average would need to be equal the space average for almost all initial states 
  
    
      
        x
        ∈
        X
      
    
    {\displaystyle x\in X}
  
, with 
  
    
      
        X
      
    
    {\displaystyle X}
  
 being the <a href="/facts/Phase_space/qPe4Fq57">phase space</a>. For an SRB measure 
  
    
      
        μ
      
    
    {\displaystyle \mu }
  
, it suffices that the ergodicity condition be valid for initial states in a set 
  
    
      
        B
        (
        μ
        )
      
    
    {\displaystyle B(\mu )}
  
 of positive <a href="/facts/Lebesgue_measure/8us9cGoW">Lebesgue measure</a>.
</p><p>The initial ideas pertaining to SRB measures were introduced by <a href="/facts/Yakov_Sinai/6hVuJDaH">Yakov Sinai</a>, <a href="/facts/David_Ruelle/mjoK3TGl">David Ruelle</a> and <a href="/facts/Rufus_Bowen/gaaHbccN">Rufus Bowen</a> in the less general area of <a href="/facts/Anosov_diffeomorphism/8SudeRhj">Anosov diffeomorphisms</a> and <a href="/facts/Axiom_A/IHHhw0DP">axiom A attractors</a>.
</p>

Sinai–Ruelle–Bowen measure open-in-new

Sinai–Ruelle–Bowen measure