ON FUNCTIONS ATTRACTING POSITIVE ENTROPY

Autor:	Ryszard J. Pawlak, Anna Loranty
Rok vydání:	2017
Předmět:	010101 applied mathematics Pure mathematics Positive entropy Lebesgue measure Dynamical systems theory Point density General Mathematics 010102 general mathematics Entropy (information theory) 0101 mathematics Fixed point 01 natural sciences Mathematics
Zdroj:	Bulletin of the Australian Mathematical Society. 97:69-79
ISSN:	1755-1633 0004-9727
DOI:	10.1017/s0004972717000855
Popis:	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 $x_{0}$.
Databáze:	OpenAIRE
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