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ORDERS OF GROWTH AND GENERALIZED ENTROPY
Published online by Cambridge University Press: 28 September 2021
Abstract
We construct the complete set of orders of growth and define on it the generalized entropy of a dynamical system. With this object, we provide a framework wherein we can study the separation of orbits of a map beyond the scope of exponential growth. We show that this construction is particularly useful for studying families of dynamical systems with vanishing entropy. Moreover, we see that the space of orders of growth in which orbits are separated is wilder than expected. We achieve this with different types of examples.
MSC classification
Primary:
37B40: Topological entropy
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 4 , July 2023 , pp. 1581 - 1613
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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