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arXiv · 1707.01760

Tropical Markov dynamics and Cayley cubic

K. Spalding·A. P. Veselov
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Abstract

We study the tropical version of Markov dynamics on the Cayley cubic, introduced by V.E. Adler and one of the authors. We show that this action is semi-conjugated to the standard action of $SL_2(\mathbb Z)$ on a torus, and thus is ergodic with the Lyapunov exponent and entropy given by the logarithm of the spectral radius of the corresponding matrix.

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K. Spalding, A. P. Veselov. 2017-07-06. Tropical Markov dynamics and Cayley cubic. https://arxiv.org/abs/1707.01760

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