On the smallest numerical semigroups closed under affine maps

Amelia Álvarez, Carlos-Jesús Moreno-Ávila, Ignacio Ojeda

We study numerical semigroups $S_{a,b}(m)$ generated by the orbit of $m$ under the affine map $T_{a,b}(z)=az+b$, where $a\ge 2$, $m>1$, $\gcd (b,m)=1$, and $b\ge -(a-2)m-2$. This ex…