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Jörg Neunhäuserer
Jörg Neunhäuserer
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It is quite easy to construct a dynamical system which has a physical measure with a positive Lyapunov exponent and zero entropy, just a figure $\infty$ system. By Pesin's entropy formula such a measure can not be a Sinai-Ruelle-Bowen measure. Now my question is, if there exists a system with a physical measure with positive entropy that is not a SRB-measure. I think the answer is Yes, but I did not manage the construction of such a system. (Perhaps I have to add that I am interested in ergodic and hyperbolic physical measures that are not SRB)

It is quite easy to construct a dynamical system which has a physical measure with a positive Lyapunov exponent and zero entropy, just a figure $\infty$ system. By Pesin's entropy formula such a measure can not be a Sinai-Ruelle-Bowen measure. Now my question is, if there exists a system with a physical measure with positive entropy that is not a SRB-measure. I think the answer is Yes, but I did not manage the construction of such a system.

It is quite easy to construct a dynamical system which has a physical measure with a positive Lyapunov exponent and zero entropy, just a figure $\infty$ system. By Pesin's entropy formula such a measure can not be a Sinai-Ruelle-Bowen measure. Now my question is, if there exists a system with a physical measure with positive entropy that is not a SRB-measure. I think the answer is Yes, but I did not manage the construction of such a system. (Perhaps I have to add that I am interested in ergodic and hyperbolic physical measures that are not SRB)

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Jörg Neunhäuserer
Jörg Neunhäuserer
  • 1.6k
  • 2
  • 14
  • 27

Physical measures that are not SRB

It is quite easy to construct a dynamical system which has a physical measure with a positive Lyapunov exponent and zero entropy, just a figure $\infty$ system. By Pesin's entropy formula such a measure can not be a Sinai-Ruelle-Bowen measure. Now my question is, if there exists a system with a physical measure with positive entropy that is not a SRB-measure. I think the answer is Yes, but I did not manage the construction of such a system.