We study a family of birational maps of smooth affine quadric 3-folds $x_1x_4-x_2x_3=$ constant, over $\mathbb{C}$, which seems to have some (among many others) interesting/unexpected characters: a) they are cohomologically hyperbolic, b) their second dynamical degree is an algebraic number but not an algebraic integer, and c) the logarithmic growth of their periodic points is strictly smaller than their algebraic entropy. These maps are restrictions of a polynomial map on $\mathbb{C}^4$ preserving each of the quadrics. The study in this paper is a mixture of rigorous and experimental ones, where for the experimental study we rely on the Bertini which is a reliable and fast software for expensive numerical calculations in complex algebraic geometry.

翻译：我们研究的是一个圆形方形平面3倍双形图的组合,其值为$x_1x_4-x_2x_3=恒定值,超过$\mathbb{C}$,其中似乎有一些(许多其他)有趣的/不预期的字符:(a) 它们具有共和性双曲,(b) 它们的第二个动态度是一个代数,但不是代数整数,以及(c) 它们周期点的对数增长绝对小于它们的代数酶酶。这些图是多元图中用于保存每个四重体的限定值。本文中的研究是严格和实验性的混合体,在实验研究中,我们依靠Bertini作为在复杂的代数几何测量中进行昂贵的数字计算的一个可靠和快速的软件。