### Electronic Research Archive

2021, Issue 4: 2819-2827. doi: 10.3934/era.2021015
Special Issues

# 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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