Abstract
We study a generalized Hénon map in two-dimensional space. We find a region of the phase space where the nonwandering set exists, specify parameter values for which this nonwandering set is hyperbolic, and prove that our map when restricted to a specific invariant subset is topologically conjugate to the Bernoulli three-shift. Coupling two such maps, as a result, we obtain a map in four-dimensional space and show that Bernoulli shifts also exist in this map.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 202-209 https://doi.org/10.4213/tmf10007.
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Anastassiou, S. Complicated behavior in cubic Hénon maps. Theor Math Phys 207, 572–578 (2021). https://doi.org/10.1134/S0040577921050032
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DOI: https://doi.org/10.1134/S0040577921050032