Pablo Sáez, Xavier Vidaux, Maxim Vsemirnov, “Endomorphisms and dynamic on the affine Büchi's quadratic <nobr>$4$</nobr> surface”, Mosc. Math. J., 2024, Volume 24, Number 3,Pages <nobr>441

Endomorphisms and dynamic on the affine Büchi's quadratic $4$ surface

Pablo Sáez^a, Xavier Vidaux^b, Maxim Vsemirnov^c

^a Independent researcher. Postal address: Calle nueva 3, Población Versalles, San Pedro de la Paz, Chile
^b Universidad de Concepcion, Chile. Postal address: Departamento de Matematica, Facultad de Ciencias Fisicas y Matematicas, Avenida Iturra s/n, Barrio Universitario, Concepcion, Chile
^c St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences. Postal address: POMI RAN, Fontanka 27, St.Peterburg, 191023, Russia

Abstract: The quadratic Büchi surface $B_4$ has affine equations $x_4^2-2x_3^2+x_2^2=x_3^2-2x_2^2+x_1^2=2$. We describe two non-trivial endomorphisms and second-order linear recurrence relations that preserve integrality on $B_4$, thus giving a way to build a forest-like structure on the set of integral points on $B_4$.

Key words and phrases: Büchi sequences

MSC: 11B83, 11D09

Language: English

DOI: 10.17323/1609-4514-2024-24-3-441-459