Ergodicity of a 2-to-1 baker map

Neemias S. Martins, Pouya Mehdipour

Resumo


We encode a 2-to-l baker map using the so called zip shift map, defined on an extended two-sided symbolic space. Moreover show that the 2-to-l baker map is a (2,4)—Bernoulli  transformation. As an application, we show that it is strongly mixing and ergodic.  


Palavras-chave


Ergodic Theory; Deterministic Chãos; Bernoulli Transformations; Zip shift map.

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Referências


Lasota. A., Mackey, M. Chãos, Fractals, and Noise, Stochastic Aspects of Dynamics, Springer- Verlag New York Tnc, volume 97, 1994.

Mehdipour, P., Lamei, S., An n-to-1 Smale Horseshoe, (pre-print-2020).

Mehdipour, P., Martins, N. Encoding an n-to-1 Baker Map, Çpre-print-2020).

Oliveira, K., Viana, M. Foundations of ergodic theory, Cambridge Studies in Advanced Mathematics, 2015.

Shub, M. What is... a horseshoe?, Notices of the American Mathematical Society, volume 52, pages 516-517, 2005.

Walters, P. An introduction to Ergodic Theory. Graduate texts in mathematics, Springer-Verlag, 1982.




DOI: https://doi.org/10.5540/03.2021.008.01.0404

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