Published: 1999-09-30

Topological transitivity for expanding monotonic mod one transformations with two monotonic pieces

Peter Raith

Abstract

Consider a continuous and strictly increasing function f: [0,1]→[0,2], and define Tfx = f(x)(mod 1). Then Tf is a monotonie mod one transformation with two monotonic pieces, if and only if f(0) < 1 < f(1). It is proved that Tf is topologically transitive, if f is piecewise differentiable and infx∈[0,1]f'(x) ≥ √2.

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Raith, P. (1999). Topological transitivity for expanding monotonic mod one transformations with two monotonic pieces. Annales Mathematicae Silesianae, 13, 233–241. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14152

Domyślna okładka

Vol. 13 (1999)
Published: 1999-09-30


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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