  We study a family of birational maps of smooth affine quadric 3-folds, {over
the complex numbers}, of the form $x_1x_4-x_2x_3=$ constant, 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 Bertini which is a reliable
and fast software for expensive numerical calculations in complex algebraic
geometry.
