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Ergodic measures of intermediate entropy for affine transformations of nilmanifolds

  • Received: 01 August 2020 Revised: 01 January 2021 Published: 22 February 2021
  • 37A35, 37B40

  • In this paper we study ergodic measures of intermediate entropy for affine transformations of nilmanifolds. We prove that if an affine transformation $ \tau $ of nilmanifold has a periodic point, then for every $ a\in[0, h_{top}(\tau)] $ there exists an ergodic measure $ \mu_a $ of $ \tau $ such that $ h_{\mu_a}(\tau) = a $.

    Citation: Wen Huang, Leiye Xu, Shengnan Xu. Ergodic measures of intermediate entropy for affine transformations of nilmanifolds[J]. Electronic Research Archive, 2021, 29(4): 2819-2827. doi: 10.3934/era.2021015

    Related Papers:

  • In this paper we study ergodic measures of intermediate entropy for affine transformations of nilmanifolds. We prove that if an affine transformation $ \tau $ of nilmanifold has a periodic point, then for every $ a\in[0, h_{top}(\tau)] $ there exists an ergodic measure $ \mu_a $ of $ \tau $ such that $ h_{\mu_a}(\tau) = a $.



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