ON FUNCTIONS ATTRACTING POSITIVE ENTROPY

We examine dynamical systems which are ‘nonchaotic’ on a big (in the sense of Lebesgue measure) set in each neighbourhood of a fixed point $x_{0}$ , that is, the entropy of this system is zero on a set for which $x_{0}$ is a density point. Considerations connected with this family of functions are l...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2018-02, Vol.97 (1), p.69-79
Main Authors: LORANTY, ANNA, PAWLAK, RYSZARD J.
Format: Article
Language:English
Subjects:
Dynamical systems
Entropy
Neighborhoods
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Summary:We examine dynamical systems which are ‘nonchaotic’ on a big (in the sense of Lebesgue measure) set in each neighbourhood of a fixed point $x_{0}$ , that is, the entropy of this system is zero on a set for which $x_{0}$ is a density point. Considerations connected with this family of functions are linked with functions attracting positive entropy at $x_{0}$ , that is, each mapping sufficiently close to the function has positive entropy on each neighbourhood of $x_{0}$ .
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972717000855