A birational map of a projective space whose intermediate dynamical degrees are all transcendental
We construct a birational map of $\mathbb{P}^d$ ($d\geq6$) whose intermediate dynamical degrees are all trancendental.
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arXiv subjects
Yutaro Sugimoto
Publications and source records attributed to Yutaro Sugimoto.
A $1$-cohomologically hyperbolic birational map of $\mathbb{P}^3$, with a transcendental arithmetic degree
We construct a $1$-cohomologically hyperbolic birational map of $\mathbb{P}^3$, with transcendental first dynamical degree. The arithmetic degree of this map at a $\overline{\mathbb{Q}}$-point is transcendental.
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The minimum value of the first dynamical degrees of automorphisms of complex simple abelian varieties with fixing dimensions
We consider the minimum value of the first dynamical degrees, which are larger than $1$, of automorphisms for prime dimensional complex simple abelian varieties. Also, we calculate the minimum value of the first dynamical degrees, which are larger than $1$, of automorphisms of complex simple abelian varieties with fixing the dimensions from $2$ to $10$.
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Dynamical degrees of automorphisms of complex simple abelian varieties and Salem numbers
We prove that every Salem number can be realized as the first dynamical degree of an automorphism of a complex simple abelian variety. Also by using the similar technique, we prove that the set of first dynamical degrees of automorphisms of complex simple abelian varieties except 1 has the minimum value when fixing the dimension of complex simple abelian varieties. Moreover, we prove that there is an automorphism of a complex simple abelian variety, whose first dynamical degree is as close as possible to 1. These results are inspired by the work of Nguyen-Bac Dang and Thorsten Herrig.
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