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ON FUNCTIONS ATTRACTING POSITIVE ENTROPY

Part of: Maps and general types of spaces defined by maps Topological dynamics Real functions

Published online by Cambridge University Press:  04 October 2017

ANNA LORANTY Open the ORCID record for ANNA LORANTY [Opens in a new window]  and
RYSZARD J. PAWLAK Open the ORCID record for RYSZARD J. PAWLAK [Opens in a new window]
ANNA LORANTY*
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, Banacha 22, 90-238 Łódź, Poland email loranta@math.uni.lodz.pl
RYSZARD J. PAWLAK
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, Banacha 22, 90-238 Łódź, Poland email rpawlak@math.uni.lodz.pl
*
✉loranta@math.uni.lodz.pl
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Abstract

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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 $x_{0}$.

Keywords

approximately continuous function0-approximately continuous functionentropy0-approximate stable point

MSC classification

Primary: 26A18: Iteration
Secondary: 37B40: Topological entropy 54C70: Entropy 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 69 - 79
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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