On N-Distal Homeomorphisms

Rego，E.1; Salcedo，J. C.2

2023-12-01

10.1007/s12346-023-00839-3

Qualitative Theory of Dynamical Systems   Impact Factor & Quartile

1575-5460

1662-3592

In this work we study N-distal properties for homeomorphisms on compact metric spaces. For instance, we define N-equicontinuity and prove that every N-equicontinuous system is N-distal. We introduce the notions of N-distal extensions and N-distal factors. We also prove that M-distal extensions of N-distal homeomorphisms are MN-distal and present a non-trivial N-distal factor for N-distal homeomorphism having Ellis semigroup with a unique minimal ideal. It is also shown that transitive N-distal homeomorphisms have at most N- 1 minimal proper subsystems. Finally, we prove that topological entropy vanishes for countably-distal systems on compact metric spaces. These results generalize previous ones for distal systems (Fürstenberg in Am J Math 85:477–515, 1963; Parry in Zero entropy of distal and related transformations, Benjamin, New York, pp 383–389, 1967).

Distal N-Distal N-Distal extensions N-Equicontinuous Topological entropy

SCI

English

First ; Corresponding

Mathematics

Mathematics, Applied ; Mathematics

WOS:001036798000001

SPRINGER BASEL AG

2-s2.0-85165715924

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
2.Instituto de Matemática,Universidade Federal do Rio de Janeiro,Rio de Janeiro,P. O. Box 68530,21945-970,Brazil

Rego，E.,Salcedo，J. C.. On N-Distal Homeomorphisms[J]. Qualitative Theory of Dynamical Systems,2023,22(4).

Rego，E.,&Salcedo，J. C..(2023).On N-Distal Homeomorphisms.Qualitative Theory of Dynamical Systems,22(4).

Rego，E.,et al."On N-Distal Homeomorphisms".Qualitative Theory of Dynamical Systems 22.4(2023).