# A rational map with infinitely many points of distinct arithmetic degrees

@article{Lesieutre2020ARM, title={A rational map with infinitely many points of distinct arithmetic degrees}, author={John Lesieutre and Matthew Satriano}, journal={Ergodic Theory and Dynamical Systems}, year={2020}, volume={40}, pages={3051 - 3055} }

Let be a dominant rational self-map of a smooth projective variety defined over $\overline{\mathbb{Q}}$ . For each point $P\in X(\overline{\mathbb{Q}})$ whose forward $f$ -orbit is well defined, Silverman introduced the arithmetic degree $\unicode[STIX]{x1D6FC}_{f}(P)$ , which measures the growth rate of the heights of the points $f^{n}(P)$ . Kawaguchi and Silverman conjectured that $\unicode[STIX]{x1D6FC}_{f}(P)$ is well defined and that, as $P$ varies, the set of values obtained by $\unicode… Expand

#### 2 Citations

Current trends and open problems in arithmetic dynamics

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- Bulletin of the American Mathematical Society
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A transcendental dynamical degree

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