Moscow Mathematical Journal

Volume 24, Issue 3, July–September 2024 pp. 441–459.

Endomorphisms and Dynamic on the Affine Büchi's Quadratic 4 Surface

Authors: Pablo Sáez (1), Xavier Vidaux (2), and Maxim Vsemirnov (3)
Author institution:(1) Independent researcher. Postal address: Calle nueva 3, Población Versalles, San Pedro de la Paz, Chile
(2) Universidad de Concepcion, Chile. Postal address: Departamento de Matematica, Facultad de Ciencias Fisicas y Matematicas, Avenida Iturra s/n, Barrio Universitario, Concepcion, Chile
(3) St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences. Postal address: POMI RAN, Fontanka 27, St.Peterburg, 191023, Russia

Summary:

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 $B_4$ .

2020 Math. Subj. Class. 11B83, 11D09.

Keywords: Büchi sequences.

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