Abstract
It is a well-known fact that Anosov endomorphisms of n-torus which are different from automorphisms and expanding endomorphisms are not structurally stable and, in general, are not conjugated to algebraic endomorphisms. Nevertheless, hyperbolic algebraic endomorphisms of torus are conjugated with their C1 perturbations on the set of periodic points. Therefore the study of algebraic toral endomorphisms is very important. This paper is devoted to study of the structure of the sets of periodic and pre-periodic points of algebraic toral endomorphisms. Various group properties of this sets of points are studied. The density of periodic points for algebraic endomorphisms of n-torus is proved; it is clarifief how the number of periodic and pre-periodic points with a fixed denominator depends on the properties of the characteristic polynomial. The Theorem 1.1 is the main result of this paper. It contains an algorithm that allows to split the sets of periodic and pre-periodic points of a given algebraic endomorphism of two-dimensional torus.
Highlights
Что в случае произвольного алгебраического эндоморфизма множество периодических и предпериодических точек может включать в себя как точки с рациональными, так и точки с иррациональными координатами
It is a well-known fact that Anosov endomorphisms of n-torus which are different from automorphisms and expanding endomorphisms are not structurally stable and, in general, are not conjugated to algebraic endomorphisms
Hyperbolic algebraic endomorphisms of torus are conjugated with their C1 perturbations on the set of periodic points
Summary
Что в случае произвольного алгебраического эндоморфизма множество периодических и предпериодических точек может включать в себя как точки с рациональными, так и точки с иррациональными координатами. Что для алгебраического автоморфизма тора (см., например, [7]) любая точка с рациональными координатами является периодической. Aq тогда и только тогда, когда для любого i = 1, t точка φpαi i (s1, ..., sn) является периодической точкой эндоморфизма Apαi i .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
