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- W2950261527 abstract "For a dominant rational self-map on a smooth projective variety defined over a number field, Kawaguchi and Silverman conjectured that the (first) dynamical degree is equal to the arithmetic degree at a rational point whose forward orbit is well-defined and Zariski dense. We prove this conjecture for surjective endomorphisms on smooth projective surfaces. For surjective endomorphisms on any smooth projective varieties, we show the existence of rational points whose arithmetic degrees are equal to the dynamical degree. Moreover, we prove that there exists a Zariski dense set of rational points having disjoint orbits if the endomorphism is an automorphism." @default.
- W2950261527 created "2019-06-27" @default.
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- W2950261527 date "2017-01-16" @default.
- W2950261527 modified "2023-10-03" @default.
- W2950261527 title "Arithmetic degrees and dynamical degrees of endomorphisms on surfaces" @default.
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- W2950261527 doi "https://doi.org/10.48550/arxiv.1701.04369" @default.
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