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ORDERS OF GROWTH AND GENERALIZED ENTROPY

Part of: Topological dynamics Smooth dynamical systems: general theory

Published online by Cambridge University Press:  28 September 2021

Javier Correa Open the ORCID record for Javier Correa [Opens in a new window]  and
Enrique R. Pujals
Javier Correa*
Affiliation:
Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos, 6627 – Pampulha, Belo Horizonte – MG, 31270-901 BRAZIL
Enrique R. Pujals
Affiliation:
The Graduate Center – CUNY, 365 Fifth Avenue, New York, NY 10016 USA (epujals@gc.cuny.edu)
*
jcorrea@mat.ufmg.br
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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.

Keywords

Dynamical SystemsTopological EntropyVanishing Entropy

MSC classification

Primary: 37B40: Topological entropy
Secondary: 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 4 , July 2023 , pp. 1581 - 1613
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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